UC  NRLF 


QB 


T 

A 

BL 

ES 

V  E 

NT 

u 

s, 

THK  AMERICAN  El'HKMERIS  AND  iNAUTICAL  ALMANAC. 


BY 


GEORGE  W.  HILL. 


BUREAU    OK    NAVIGATION, 

\V  A  s  il  |  N  <;  To  X. 
18 


\  -'University  of  California. 


.  HFT    OF 


TABLES 


OK 


VENUS, 


I'RKPARKJ)   I'T>R  Till.   HSK.  Ol' 


THE  AMERICAN  EPHEMERIS   AND  NAUTICAL  ALMANAC 


BV 


GEORGE   W.    El  ILL. 


I'unusur.n  BV  AUTHORITY  OK  THE  SECRETARY  OK  THK  NAVY. 


BUREAU   OF   NAVIGATION, 

WASHINGTON. 

1872, 


PBEFACE. 


Tin:  following  tallies  of  Venus  have  liccn  prepared  to  take  the  place  of  the  unsatisfactory 
elements  and  tallies  heretofore  used  in  the  preparation  of  tho  Antrrirtni  I''/>l/rn/"i-ix  <nnl 
.\tnif iral  AlnniiHti-. 

The  elements  given  in  Li:  VKIMMKH'S  Aitmilr*  <!<•  FObserwttoire  Inij>cri(il  tie  I'tirix,  Tome 
\'l.,  have  heen  corrected  by  the  discussion  of  au  extended  series  of  observations;  Lr. 
VKUUIKU'S  e.\]iressions  for  the  perturbations  have  been  modified  by  changes  in  the  adopted 
values  of  the  planetary  masses;  and  the  tables  have  been  carefully  arranged  so  as  to 
facilitate  the  computation  either  of  particular  places,  or  of  an  Kphemeris,  of  the  planet. 

The  work  has  been  performed  by  .Mr.  (ii:oi;cK  W.  HILL,  who  has  long  been  one  of 
I  he  most  elh'cient  Assistants  in  the  preparation  of  tho  works  published  by  this  office. 

J.  H.  C.  COFFIN, 

Prof.  Mat}/.  ('.  .V.  Ar., 
Superintendent  nf  Xtiufira/  Alnmnnr. 
WASIIIXCTOX,  May, 


S  T  E  \  T  S  . 


IxTKoprcTio*.     C+mjtrmctum  fmJ  «j»  tf  tkt  TmUf*  .  t 

EI*iD«DUofU«:Ocbltof\>B«,l?oOjO     .  I 

Prece«i»o«  of  the  iqmimmti  .                  * 

Have*  of  the  pbaeto  t 

Varriag  el«»»»t»  rf  the  ettit  mfVcmm*  ...                           .        .        .          1 

3 

.  .......           4 


. 

Arptaentt  oflht  tabl**  .6 

OWMjoitr  of  Ux-  rrlipuc  «id  ngtiUon     ......  C 


of  a  fixed  4ate    .  . 

1  to  XV                                         .......  9 

XVI  to  XXV  .        .            !• 

XXVI   :      XXXV                   -     _                            ....  .11 

«               XXXVI  to  XL                                                       .                                                          •  li 

XLI  t,  XLVI  13 

Dmrti»m*ftr  Ik'  mtt  if  tJki  TfUtt  14 

Euapie               .        .                                                            ...  .         .        W 

TrauitofV«N*iB  1761                                                     .........  VI 

«    '    •  1769    .                                                                         .  *i 

CWratiw  •)  tin  rlrmtmtt  ^  (ftc  fr*it  *f  I'tmm*      ...  *1 

L<-\rmrr"«  rlffm«»t»  »f  tfce  ortm  of  Vrnn*           .......  21 

1769          -                                     ....  2J 

r  part  •*  the  orfcit  .         .  34 

rpartof  theorfcii  * 
itbel 

31 

Sonul  nnatiau  34 


Ooroltabon  ei  MeicwT  by  Ve 

TABLE& 

T»blr 


14 
IT 

- 
I? 


i  CONTENTS. 

Page. 

Table-       .    \.\VI.    l.ii^arillllll   iil'llic  elliptic  radius  vector           .            .                                                             ......  4<> 

X.NVII.  iii  \\.\VI.  Perturbation*  of  log  r                                                                                       ....  51 

XXXVII.,  XX  Will.  Perturbations  of  the  latitude Oi 

XXXIX.    Values  <>t'A"x,  A'j,  &c.,  iind  Arg.s.  XV.  :ind  XVI  for  tliu  beginning  of  each  year  .....  ?'J 

,\l..  Corrections  of  £TZ,  fy,  &c.,  due  to  lunar  Natation      ..........  7(i 

XLI.                           "     "     "       "     due  to  sular  -Nnlation 77 

XLII.   Kai  tors  lor  finiling  corrections  of  x,  y,  z,  due  to  perturbations  of  the  latitude 7tj 

XI, HI.  1'arallax  and  semidiiiiuetcrs     ...............  "8 

XI. IV.  Motions  of  the  Argumentg  for  centuriei      ............  79 

XLV.  A  trnn  of  lung  p'-riod  in  the  perturbation  of  the  longitude    .........  80 

Xl.VJ.   Reduction  to  tlie  Ecliptic ....  80 


'UNIVERSITY! 


INTRODUCTION. 


CONSTRUCTION    AND    USE    OF    THE    TABLES. 


THE  Tables  arc  based  on  ihe  following 

Epoch,  1850,  Jan.  0.0,  Washington  Mean  Time. 


L'  =  244  18  18.32 
-'  =  129  27  42.86 
&'  =  75  19  53.10 
V  =  3  23  35.01 
c'  =  0.006843113 
n'  =  2106611".35447 

Those  elements  have  heen  derived  from  a  discussion  of  the  data  furnished  by  the  transits  of  Venus  in  1761 
and  1769,  and  by  observations  made  at  Greenwich  in  the  interval  1836-1870,  at  Paris  in  the  interval  1S38-1866, 
and  at  Washington  in  the  interval  1863-1867.  In  this  discussion  the  Solar  Theory  of  HANSEN  and  OLUFSKN  was 
used.*  Consequently  these  Tables  should  be  used  in  conjunction  with  the  Tables  du  Soleil  of  these  authors.! 

The  value  of  the  Precession  of  the  Equinoxes,  according  to  PETERS,^  is 

•  50".2411  1  +  0".0001134<2, 

where  the  unit  of  t  is  the  tropical  year,  and  it  is  counted  from  1800.     If  we  make  the  unit  the  Julian  year,  and 
count  t  from  1850,  the  formula  will  be 

50".25351  t  +  0".0001134  t2. 
The  formulae  which  define  the  motion  of  the  plane  of  the  ecliptic  are,  according  to  HANSEN  and  OLUFSEN,§ 

sin  i"  sin  Q"  =  +  0".053916  t  +  0".00001887  <2, 
sin  i"  cos  Q"  =  —  0".467839  t  +  0".00000562  f. 

In  order  to  obtain  the  tropical  motion  of  the  planet,  it  is  necessary  to  add,  to  the  sidereal  motion,  the  preces- 
sion, and  the  small  term, 

—  £  sin  i'  sin  i"  sin  (  Q'  —  Q"), 
the  numerical  value  of  which  is  +  0".01382  t.     This  it  is  also  necessary  to  add  to  the  longitude  of  the  perihelion. 

*  Tallies  du  Solril,  riiruttis  il'ii/irls  les  ordres  dc  la  SociM  Royalc  tics  Sciences  de  Copenhafrue,  par  MM.  I'   .1.  llnnsrn  et  C.  F. 
R.  Olufsen.     Co/Hiili(i<?if       1~">:5. 

I  Tlic  Pulkowa  constant  of  aliorration  20".44.">1  should  however  be  employed  instead  of  20"  i">."i. 
t  Peters'  JVumerus  Cunsluns  A'ututionis,  p.  71  §  Tables  du  Soleil,  p.  21. 

1 


INTRODUCTION. 

The  values  of  the  planetary  masses,  adopted,  are 

Mercury  =    i^;.---,),  Mars  ;»'"  =   •{.)()()()()()' 


Venus  m'  =  Jupiter  »tlv  =       inr.ri    ' 

'iUOl'Vl  »\7«JU 


The  Earth  and  Moon    w"  =    .j;,.,^/,,, ,  Saturn 


Tlic  mass  of  Mercury  is  that  of  ENCKE,*  the  mass  of  the  Earth  and  Moon  is  that  found  hy  Prof.  S.  NEWCOMB,! 
and  which  corresponds  to  the  value  8".  848  of  the  mean  horizontal  parallax  of  the  Sun  ;  the  values  of  the  other 
masses  arc  those  adopted  by  HANSEN  and  OLUFSEN.  On  these  values  of  the  disturbing  masses  depend  the  expres- 
sions of  the  secular  and  periodic  perturbations  used,  with  the  single  exception,  that,  since  the  discussion  of  the 
observations  inc!>c.it<  d  32".  515  as  ihe  value  of  the  annual  tropical  motion  of  the  node,  this  value  has  been  preferred 
to  the  value  32//.2!).il.  given  by  theory.  If  \ve  suppose  that  the  modification  of  the  values  of  the  masses,  necessary 
»<>  |>i"j.liiot:  the  li'-:-i  number,  should  be  applied  to  Venus  alone,  the  mass  of  this  planet  would  be  reduced  to 

1 
421240  ' 

Thus  the  following  are  the  expressions  of  the  varying  elements,  the  longitudes  being  referred  to  the  mean 
equinox  and  eeliplie  of  date,  and  /  reckoned  from  1850,  Jan.  0.0,  Washington  Mean  Time:  — 

L'  =  241  18  18.32  +  2  10669  L62  180  t  +  o!'o001134  t2, 
-'  =  129  27  42.86  +  50.0494  t     -  0.000592  t\ 

&'  =    75  19  53.10  +  32.5150  t     +  0.000151  t*, 

i>    =       3  23  35.01  +  0.03814  t  —  0.0000016  /,2, 

e'  =      0.006843113  —  0.00000050009  /  +  0.0000000000128  <2, 
=       1411".494  -  0".10315  t  +  0".00000265  t?. 


The  value  of  the  semi-axis  major  of  the  planet's  orbit  is  given  by  the  equation 

a,  =  rl±j2L.  *"l»  «// 

LI  +  m"    n'-J 


To  be  consisient,  \ve  must  employ  the  same  linear  unit  for  the  radius  vector  of  Venus  as  that  which  HANSEN 
and  OUTFSKN  have  used  for  the  radius  vector  of  the  Earth.  From  an  examination  of  their  formula-,  it  appears 
that  they  have  taken  as  unity,  not  n",  but,  in  the  notation  of  LAPLACE,  the  quantity 


I  denoting  summation  with  respect  to  all  the  masses  which  produce  sensible  perturbations  in  the  motion  of  the 
Earth.     Hence  their  value  of  a"  is 

,   v       ,/2   d  A^ 

|-*1"-*I5»   ' 

And,  the  numerical  values  being  substituted,  we  obtain 

log  a"  =  9.9999998786. 
The  tropical  motion  of  the  Sun,  in  a  Julian  year,  is,  according  to  the  Tables  du  Soldi,  equal  to 

360°  —  22".56009  —  0".380853  X  0.01677  +  50".23414. 
If  from  this  is  subtracted  50".25351,  our  value  of  the  precession,  the  value  of  «",  we  adopt,  is  obtained, 

n"  =  1295977".41415. 
And  consequently, 

log  a'  =  9.8593376699. 

*  .l.tlriiiiiiniisr/ii-  .Viirliririttrn,  J\"o.  443. 

t  Astronomical  and  XMiarologtcal  Observations  made  at  the  United  States  Naval  Observatory  during  the  year  1865      Appendix 

u.,  p.  ao. 

2 


I  INTRODUCTION. 


Tin;  expression  of  the  equation  of  the  ccntn-,  for  llir  epoch  1S5P.O,  is 

+  2822".971  sin  .V  +  12".071  sin  2  M  +  0".072  sin  :;  M. 

Tin-  expression  of  the  logarithm  of  the  elliptic  radius  vc-rlor  for  llie  same  time  is 

9.8593127  is  -  0.00-2971871  cos  ji/  -  o.ooooi5253  cos  -2  M  -  0.000000099  cos  3  ,u. 

The  elliptic  heliocentric  latitude  referred  to  tin;  ecliptic  of  date  may  be  found  from  the  formula 

log  sin  1,-it.  =  8.7722149  +   13.51  /  +  log  sin  [orh.  Ion-.  +  (360'  -   Q')]. 
The  secular  perturbation  of  the  orbit  longitude  is  given  In   the  formula, 

(  -  0".  12691  sin  ,17  -  0".0()1()S  sin  -I  M)  in. 
IU  ilciiotini;  the  number  of  anomalistic  revolutions  of  llic  planet  from  the  epoch. 

The  secular  perturbation  of  the  logarithm  of  the  radius  vector  is  -riven  by  the  formula,  (in  units  of  llic  eighth 

decimal), 

(  —  0.016  +  13.360  cos  M  +  0.137  ens  •>  .\f  )  in. 

The  following  are  the  expressions  lor  the  periodic  perturbations  of  Venus;  /.  /'  iVc.  denoting  (he  mean  longi- 
tudes of  the  several  planets  in  their  order,  referred  to  the  mean  equinox  of  1850.0.  They  have  been  obtained  bv 
multiplying  the  expressions  given  in  Li:  YKKKIKK'S,  •'  Aiuiuli  '*  ilc  /'  (ilwn-uluii-c  l/ii/in-in/  i/r  i'tirix"  Tonic  VI, 
by  the  pmper  faciors. 


Perturbation*  n/'  //«•  (>/-/:ii  \.<ni>:\imli-. 


ACTION  or  MI.KCURY. 


+  0.011  sin  (/  -  /') 
—  0.010  sin  -2  (I  -  /') 
-  0.005  sin  :i  (/  -  /') 
4-  0.0:21  sin  (2  I  —  I1  +  281°) 


4-  0.328  sin  (/  —  2  /'  +  251°.8) 
4-  0.015  sin  (2  /  -  3  /'  4-  7  I  ) 
4-  0.047  sin  (3  /'  -  /  +  35°) 
4-  0.139  sin  (-Z  I  —  4  /'  4-  .'WH".3) 
4-  0.453  sin  (2  /  —  5  /'  4-  35°.  1). 


ACTION  OF  THE  EAISTII. 


—  4.!)81  sin  (/'  -  /") 

-  11,189  sin  -Z  (/'  -  /") 

4-  7.-260  sin  (3  /'  -  3  /"  4-  0°  7'.6) 

4-  1.050  sin  (4  /'  -  4  /"  4-  0D    10') 

4-  0.3:!5  sin  (5  /'  -  5  /"  4-   1°.5) 

4-  0.143  sin  6  (/'  -  /") 

4-  0.0(57  sin  7  (/'  -  /") 

4-  0.035  sin  8  (/'  —  /") 

4-  0.0 19  sin  <)(/'-/") 

+  0.013  sin  10  (/'  —  /") 

4-  0.007  sin  11  (/'  -  /") 

+  0.004  sin  12  (/'  -  /") 

4-  0.003  sin  13  (/'  -  /") 

4-  0.059  sin  (4  /'  -  3  /"  4-  227°.7) 

4-  0.099  sin  (3  /'  —  2  /"  4-  53V2) 

4-  0.019  sin  (-2  /'  —  /"  4-  51°) 

4-  0.070  sin  (/"  4-  109°.2) 

4-  0.093  sin  (-2  /"  -  /'  4-  18°.2) 

4-  3.515  sin  (-2  /'  -  3  /"  4-  208°  7'.f>) 


4-  0.687  sin  (3  /'  -  4  /"  +  268°.  1) 
4-  1.620  sin  (4  /'  —  5  /"  4-  '268°  24'.5) 
4-  0.210  sin  (5  /'  —  6  /"  4-  89°.5) 
4-  0.055  sin  (6  /'  —  7  /"  4-  89°) 
4-  0.0-24  sin  (7  /'  —  8  /"  4-  88°) 
4-  0.013  sin  (8  /'  —  9  /"  4-  90°) 
4-  0.0-2-2  sin  (-2  /"  4-  210°) 
4-  0.044  sin  (3  /'•  —  /'  4-  53°) 
4-  1.495  sin  (5  /"  -  3  /'  4-  198°  21') 
4-  0.188  sin  (4  /'  —  fi  /"  4-  340°.7) 
4-  0.096  sin  (5  /'  -  7  /"  4-  337°..r>) 
4-  0.155  sin  (6  /'  —  8  /"  4-  163°.l) 
4-  0.015  sin  (7  f  -  9  /"  4-  160°) 
4-  0.013  sin  (5  /"  —  2  /'  +  77°) 
4-  0.218  sin  (5  /'  -  8  /"  4-  66°.5) 
4-  0.013  sin  (7  /'  —  10  /"  4-  67°) 
4-  0.067  sin  (9  /'  —  13  /"  +  346".2) 
+  2.820  sin  (8  /'  —  13  /"  4-  227  '   5S') 
4-  0.026  sin  (13  /"  -  7  /'  4-  198°). 


INTRODUCTION. 


ACTION  OF  MAI:S. 


—  0.0  IS  sin  (/'  —  I1" 

+  0.0.-)!)  sin  2  (/'  —  /"') 

4-  0.019  sin  (/'  —  2  I1"  +  155°) 

+  0.657  sin  (2  /'  -  3  /"'  4-  332° 


sin  (/'  -  /'-'  +  0°  31') 
+  0.8SO  sin  2  (/'  -  /iv) 
+  0.0-11  sin  3  (/'  —  /iv) 
+  0.007  sin  4  (/'  -  /iv) 
4-  0.0-26  sin  (2/'  -  /'v  4-  113°) 
+   1.557  sin  (/iv  +  169°  507) 


—  0.178  sin  (/'  -  /v) 
.f-  0.050  sin  '2  (/'-  /"] 


4-  0.009  sin 
+  1.168  sin 
4-  0.019  sin 
4-  0.021  sin 
+  0.08-2  sin 


(3  //  _  4  P"  +  333°) 
(//  _  3  /"'  4-  1 17°  56') 
(2  /'  _  4  /"'  +  1^6°) 
(3  /'  -  6  /'"  +  281°) 
(o  //  _  fi  ////  +  740.8). 


ACTION  OF  Jui'lTER. 


+  0.477  sin 
+  0.167  sin 
+  0.019  sin 
4-  0.094  sin 
+  0.055  sin 
+  0.046  sin 
+  0.027  sin 


ACTION  OF  SATURN. 


+  0.205  sin 
4-  0.025  sin 
+  0.010  sin 


(/'  _  2  /iv  +  155°.6) 
(2/'  -  3/iv  +  12°.  1) 
(3  //  _  4  /»•  +  12°) 
(//  4.  /iv  4.  o°.3) 
(2  /iv  +  143°) 
(//  _  3  /*  4-  164°) 
(2  /'  -  4  /iv  4.  2-\°). 


(/v  +  190°) 

(2  /'  -  3  r  +  90°). 


of  I  In:  aeronil  onlrr,  depending  on  the  product  of  t  lie  musses  of  Ike  Earth  and  Mars. 
+  0".282  sin  (4  /'"  4.  3  /'  -  7  /"  +  147°.  1). 


]'i-rturbation.i  of  tin'  Common  Logarithm  of  the  Radius  Vector,  in  units  of  the  eighth  decimal. 

ACTION  OF  MERCURY. 


+  4.3 

4-  8. 1  cos  (/  —  /') 

4-  1.1  cos  2  (/-  /') 

4-  6.1  cos  (2/-  /'  +  285°) 

4-  4.3  cos  (/'  +  105°) 


4-  15.3  cos  (2  /  —  4  /'  4-  150°.7) 
+  22.2  cos  (/  —  2  /'  4-  75°.  1) 
+     1.9  cos  (2  /  -  3  /'  4-  75°) 
+     3.5  cos  (3  /'  -  /  4-  -207°) 
4-     7.5  cos  (2  /  -  5  /'  +  226°). 


ACTION  OF  THE  EARTH. 


-  18.6 

4-  228.2  cos  (/'  —  /") 
4;  998.6  cos  2  (/'  —  /") 

-  si  1.8  cos  (3  /'  -  3/"  +  0°  8') 

—  145.2  cos  1  (/'  -  /") 

-  52.2  cos  (5  /'  -  5  /"  4-  0°  20') 

—  23.0  cos  6  (/'  —  /") 

—  11.5  cos  7  (/'  —  /") 
-       6.4  cos  8  (/'  —  /") 

—  3.5  <-os  9  (/'  -  /") 

—  2.6  cos  10  (/'  -  /") 

4-       7.2  cos  (4  /'  -  3  /"  +  45°) 
+     11.7  cos  (3  /'  —  2  /"  +  230°.5) 
+      6.6  cos  (2  /'  —  /"  +  230°) 
+       3.1  cos  (/'  4-  105°) 


+      4.7  cos  (/"  4-  286°) 
4-      3.2  cos  (2  /"  —  /'  4-  114°) 

4-  76.8  cos  (2  /'  -  3  /"  4-  89°.8) 

4-  46.1  cos  (3  /'  -  4  /"  +  88°.9) 

4-  162.2  cos  (4  /'  -  5  /"  +  88°  52') 

4-  25.6  cos  (5  /'  -  6  I"  +  268°.7) 
4-       7.7  cos  (6  /'  —  7  /"  4-  268°) 
4-       4.2  cos  (7  /'  -  8  I"  4.  ^70°) 
4-       3.7  cos  (2  /"  +  30°) 
+       4.5  cos  (3  /"  —  /'  4-  249°) 

+  17.2  cos  (5  /"  —  3  /'  4-  21°.8) 
+  7.2  cos  ( 1  /'  _  6  /"  +  159°) 
+  7.1  cos  (5  /'  —  7  /"  4-  172°) 

4-  17.2  cos  (6  /'  -  8  /"  +  338°.2) 
4-  6.9  cos  (9  /'  —  13  /"  +  158°) 
+  2.4  cos  (13  /"  —  7  /'  4.  25°). 


INTRODUCTION. 


+  3.5  cos  (/'  —  /'") 
—  7.9  cos  2   /'  —  I"1) 


—    19.-2 

4-  299.2  cos  (/'  —  I*  4-  0°  'JO') 
-  I33.it  cos  -.'  (/'  —  /iv) 
7.0  coa  3  (/'  —  flv) 
+       1.1  cos  (:>/*  —  /iv  4-237°) 


4-  is.7  coa  (/'  —  /'• ) 
—  4.3  cos  2  (/'  —  /v) 


[OH  oi-  MA  IIS. 

4-  (is.i  coa  (•*>!'  —  3  i'"  +  i.vr.ii). 

ACTION  OF  JUI-ITKR. 

-f-    N.8  cos  (/iv  4-  352°) 

+  10. 9  cos  (/'  —  2  /"'  4-  335°.0) 

4-  -2  l.s  coa  (-2  /'  —  3  /lv  4-  192".  l) 

4-     !).(!  cos  (/'-)-  /"'  4-   1N2  ) 

_(_    i.i  ,,,s  (/'  —  3/lv  +  3 

ACTION  oi-  SATIIKN. 


of /In-  Latitude. 
ACTION  OF  THE  EARTH. 


+  O.Ol'-i  sin  (','  /'  —  \i  I"  +  175°) 
+  O.OK!  sin  (3  /'  —  3  /"  +  356°) 
-f  0.013  sin  (4  /'  —  3  /"  +  •- 
4-  0.0-2G  sin  (3  /'  —  -^  /"  4-  -. 
4-  0.07S  sin  (-J  /'  —  /"  4-  '285°) 
4-  0.1-J1  sin  (/'  +  104°.5) 
4-  0.09-2  sin  (  -2  /"  —  /'  4-  10  I  .5 


4-  0.075  sin  (-2  /'  —  3  i"  4-  75°.r,) 
4-  0.081  sin  (3  V  —  4  /"  4-  75°.5) 
4-  0.308  sin  (4  f  —  5  I"  4-  75°.3) 
4-  0.050  sin  (5  /'  —  6  /"  4-  2r((; ') 
4-  0.014  sin  (6  /'  —  7  I"  -\-  -2-580) 
4-  0.020  sin  (3  /"—  /'  4-  '20°) 
4-  0  0-28  sin  (6  /'  —  8  /"  4-  343°) 
4-  0  .015  sin  (9  V  —  13  I"  4-  14311). 


ACTION  OF  JUPITER. 


4-  0.0-20  sin  V  —I"  4-  153°) 
4-  0.159  sin  (/'  —  '2  /lv  4-  Cl°.8) 


4-  0.023  sin  (V  4-  I™  4-  284°) 
4-  0.018  sin  (/'  —  3  /iv  +  74°). 


ACTION  OF  SATURN. 
4-  0".017  sin  (V  —  2  /v  4-  28°). 
The  tropical  motion  of  Venus  in  diflbrc-nt  intervals  of  time,  for  the  epoch  1850.0,  is, 


in  one  mean  solar  day 
in  3(i5     "         "     days 
in  366     "         "     days 
in  100  Julian  years 


1  36  7.807315, 
224  47  29.669971, 
2'26  23  37.477286, 
199  12  42.180000, 


in  100  Julian  years  less  one  day  197  36  34.372685. 

Denoting  by  d  the  number  of  days  elapsed   from  the  epoch  (1850,  Jan.  0.0,  Washington  mean  time),   the 
values  of/,  /',  <Scc.,  are — 

/  =  32 1°OG5G  +  4?0923387467  d. 

I'  =  211.3050  4-  1.6021304695  ,1. 

1"  =  100.0159  4-  0.985609 1-2-2M  d, 

I'"  =    83.2669  +  0.52 1032N5  15  d. 

/iv  =  159.9594  4-  0.083091276-2  ,1. 

/v  =     14.8203  4-  0.0331596753  d. 
5 


INTRODUCTION. 

The  Arguments  employed  in  these  tables  have  severally  the  following  meanings:— 

The  Argument  m  is  an  integer,  which  denotes  the  number  of  times  Venus  has  passed  through  its  perihelion 
since  the  beginning  of  1850;  it  is  negative  before  ibis  epoeh.  and  remains  constant  during  an  anomalistic  revolu- 
tion of  tho  planet. 

Argument  I   is  the  number  of  menu  solar  days  since  M  =  0°. 

II   is  the  number  of  Julian  years  since  8  I'  —  13  /"  -(-  318°  47'  =  0°. 
"     •  III  is  the  number  of  mean  solar  days  since  j"  — -  .'!  V"  =  0°. 
"       IV  is  the  number  of  mean  solar  days  since  5  /"  —  3  /'  -f-  288°  27'  =  0°. 
''         V  is  the  number  of  mean  solar  days  since  2  I'  —  3  /"  =  0°. 
"        VI   is  the  number  of  mean  solar  days  since  I'  —  /"  =  0°. 
"      VII  is  the  number  of  mean  solar  days  since  4  /'  —  5  /"  -j-  1°  50'  =  0°. 
"    VIII   is  the  number  of  mean  solar  days  since  2  V  —  3  I'"  +  65°  32'  =  0°. 
"       IX  is  tiic  number  of  mean  solar  days  since  V  —  7IV  =  0°. 

X   is  the  value  of?,  when  last  /'  =  129°  27  14".5,*  in  parts  of  60  to  a  circumference. 
"        XI  is  the  value  of/",  when  last  V  =  129°  27'  M".5,  in  parts  of  210  to  a  circumference. 
"      XII  is  the  value  of/"'  when  last  /'  =  129°  27'  1  l".f>.  in  parts  .if  GO  to  a  circumference. 
'•     XIII  is  the  value  of /iv,  when  last  /'  ==  129°  27'  14".5,  in  parts  of  60  to  a  circumference. 
"     XIV  is  the  value  of  ?v,  when  last  /'  =  129°  27'  14".5,  in  parts  of  36  to  a  circumference. 

•'  .    XV   is  Arg.  XI  -{-  Arg.  XIII  -j-  0.22  -|-  day  of  the  year,  of  Hanscn  and  Olufsen. 
"     XVI   is  Arg.  I  -j-  0  22052  -f-  0.01791  -f-  day  of  the  year,  of  Hanscn  and  Olufseii. 

Arguments  X — XIV  remain  constant  during  a  period  of  Argument  I,  and  are  augmented,  in  each  case,  by  a 
certain  fixed  quantity,  when  Venus  passes  through  its  perihelion  and  m  is  increased  by  a  unit. 

From  the  data  previously  given,  are  readily  obtained  the  following  expressions  for  the  value  of  the  different 
ari;iiinents;  i  denoting  an  integer,  in  general  so  taken  that  the  Argument  may  be  less  than  its  period: 

I   =  71'1.G81535  +  d  -j-  0''.0000001224  t2  —  22  I'1. 700777864  ul,t 

II  =  167V.9            +  /  —  238-V.92  i, 

III  =  11H01'».26          +  d—  11987'V25?, 

IV  =  ir/T'Ua?        -f  d  —  2959a.209  i. 
V  =  762d.072        +  d  —  1454d.9358  i, 

VI  =  234d.0375  -\- d  —  583rt.92137  i, 

VII  =  80d.466  -j-  rf  —  243d.  16487  i, 

VIII  =  186d.467  +  d  —  220d.56628  i, 

IX  =  55d.526  -f-  d  —  236d.99191  i, 

X=  5.1 167  +  33.25863  MI  —  60  ,, 

XI  =  19.5741  +  147.64477  m  —  240  i 

XII  =  7.6168  +  19.62509  m  —  60  i, 

XIII  =  25.6671  +  3.11178m  —  60  i, 

XIV  =  1.2122  +  0.75181  m  —  36  i, 
XV  =  4037d.4   -f  d  —  6798d.262  i, 

XVI  =  ld.64  +  d  —  365'1.24219  i. 

The  values  of  the  obliquity  of  the  ecliptic  and  of  the  nutation,  employed  ill  thoso  Tables,  arc  those  given  in 
the  Tables  du  So/ciV, 

e  =  23°  27'  31".42  —  0".46784  t  —  0".000001405  *2, 

J  <;•   =  —  17".332  sin  Q  (    +  0".208  sin  2  Q       --  1''.254  sin  2  Q, 
J  i         -f-  9".271  cos  S  ^   —  0".089  cos  2  Q  ^    +  0".551  cos  2  Q, 
Q,       being  the  longitude  of  the  Moon's  ascending  node,  and  Q  the  Sun's  true  longitude. 

Tliis  is  tlic  value  of  tliu  longitude  of  the  perihelion  ut  the  epoch  1850.0,  which  was  employed  in  computing  llie  tables  of 
the  perturbations  to  double  entry. 

t  Rigorously,  the  Argument  which  should  be  employed  as  the  horizontal  Argument  of  tlie  tables  of  perturbations  to  double 
entry,  lias  this  expression, 

7  I'UMMI  +tl  —  224'1.7<>080I100  m, 
But  Argument  I  may  safely  be  used  in  Its  stead,  as  thr  emir,  iu  llic  interval  from  850  A.  I),  to  2850  A.  D.  cannot  exceed  0".()05' 

6 


INTRODUCTION. 

The  reetaiiL'ular  coordinates  of  a  planet,  referred  to  the  equinox  and  equator,  are  most  readily  computed  by 
means  of  the  formula* — 

X  =  /.\  /'  sin  (/.  4~  h\)  4~  /'»  "  i''i 

y  =  A\  /'  sin  (/.  4"  ^"y1  +  1>. 

z  =  k,  r  sin  (/.  4-   A',.)  4-  pf  n  ,1, 

uhere  /.  is  ihe  orbit  longitude,  and  <"•  ,i  the  perturbation  of  the  latitude,  expressed  in  parts  of  the  radius 

The  quantities  A\,  A",,  iVc..  are  obtained  from  the  following  formula): — 
Find  /i,  //,  if.  <!  from  the  equations 

/i  sin  //  =  sin-        sin  ;!  8;  "  S'M  ^  =  s'"  *  cos  8' 

A  cos  //  -=  sin  /  sin  8?  g  cos  G  =  1 — 2  sin1'   —  cos'-'8i 

& 

then 

A-x  sin  A'x  =  1  —  '2  siir    '  sin2  8^  *y  s'n  ^y  =  '*  sin  (  H  +  ')i 

/.\  cos  A'x  =  /(  sin  H,  A-y  cos  ATV  =  g  cos  (G  4~  ^), 

k,  sin  A",,  =  —  h  cos  (H  4-  J)i 

A-zcos  Kt  =        g-  sin  (G  4~  ')• 

The  values  of  /\,  f\  and  /(z  arc,  A'  denoting  the  longitude  reduced  to  the  ecliptic, 

^>x  =  —  r  sin  ,5  cos  /.', 

]>y  =  —  r  sin  ft  cos  s  sin  //  —  r  cos  /9  sin  e, 

;;„  =  —  /•  sin  'J  sin  ;  sin  /.'  4~  r  cos  ft  cos  e. 

These  formula;  avail  for  obtaining  .1-,  (/,  and  :  relV'rred  to  any  equinox  and  equator,  provided  that  the  longitudes 
/!,  8  al'('  I'l'ferred  to  the  same  equinox,  and  the  proper  values  are  assigned  to  the  inclinations  i  and  e. 

Rut  when  the  values  of  /tx,  JTX,  &c.,  have  been  computed  for  mean  equinox  of  date,  the  effect  of  nutation  on 
these  quantities  will  be  most  easily  computed  by  the  aid  of  these  differential  coefficients, 

d.  log  A-j  _  ft 


=  _         .  cos  (Kj  _  K^  y   =     ,  sn  (r  _ 

Ky  fty 

COB  *-  *X 


,.,  - 


^      =   _  2   sin2  .j  sin  (  JTS  +  2  Q  ), 

48*. 


cos  .  gin 


^j?y      =     1    fa  sin2  1  cose  cos  (Ks  4-2  a)  4-  sin  t  sin  e  cos  (Arv  4-  8)1, 
d  Q  k,f    L  2  J 


*  gin  (^  _|_  2  Q  )  _      sin  f  cos  £  sin  (  ATZ  4- 


8  A'z  L 

^z      =      -     f'2sinz  y  sine  cos  (A'z  4-2  8)  —     sin  i  cos  £  cos  (Kz 
rf  8  kz    L 

where  3f  denotes  the  modulus  of  common  logarithms.     In  computing  the  variations  of  log  ix,  log  ky,  and  log  A-z, 
J  ;  and  J  ft  or  J  <•  must  be  expressed  in  parts  of  the  radius. 

In  computing  the  aberration,  the  constant  of  Struve  should  be  used.     The  aberration  time  is  then  given  by 
the  formula,  J  being  the  distance  of  the  planet  from  the  Earth. 

log.  aberration  time  in  days  -—  7.76052  4~  '°g-  J- 

7 


INTRODUCTION. 

The  parallax  is  given  hy  the  formula 


and  the  semi-diameter  by  the  formula 


„  8".848, 

parallax   = 


.   ,.  8". 516. 

semi-diameter  =  — 

A 


In  the:  computation  of  the  perturbations  produced  by  Venus  on  other  planetary  bodies,  the  values  of  the  incli- 
nation of  the  orbit  and  the  longitude  of  the  ascending  node  referred  to  the  ecliptic  and  equinox  of  some  fixed  date 
are  needed;  also  the  reduction  of  the  longitude  to  this  ecliptic  and  equinox  is  wanted.  If  the  current  time  be 
1850  -f-  /,  and  the  fixed  date  1850  -f-  *„,  and  c''  denote  the  general  precession  from  1850  to  1850  -)-  <,  and  /.  denote 
the  nrbit  longitude,  and  <!'0  denote  the  general  precession  from  1850  to  1850  -(-  <„,  the  formulae,  we  are  in  quest 
of.  are 

i0  =    i  —  0".06634  (t  —  /„), 
ao  =  «  —  (c-<  —  c\,)  +  7".8616  (/  —  ta), 

;.0  =  ;.  —  (v-  —  c'<0)  —  0".oi382  (t  —  /,,). 

Or,  with  sufficient  accuracy  for  our  purpose, 

i0  =    3°  23'  35"  +  0".03814  t0  —  0".02820  (/  —  *0), 
«„  =  75°  19'  53"  -4-  32".515  ta  —  9". 882  (t  —  /„), 
;.0  =  ;.  —  50".273  (t  —  O- 

In  the  American  Ephcnieris  the  heliocentric  coordinates  of  the  planets  are  given,  for  the  purpose  of  the  com- 
putation of  special  perturbations,  referred  to  the  ecliptic  and  equinox  of  the  2400000th  day  of  the  Julian  period, 
and  of  every  5000th  day  thereafter.  If  d  denote  the  number  of  days  between  the  epoch  and  the  current  time,  (it 
will  be  negative  when  the  current  time  is  before  the  epoch,)  the  formulae  for  the  computation  of  these  coordinates, 
for  Venus,  are ; — 

Epoch  =  2400000th  day  of  the  Julian  Period  =  1858,  Nov.  16. 

;,o  =  ;.  —  0".  13763d, 

x0  =  [9.99929]  r  sin  (/>0  -4-  89°  58'  32"), 

yo  =  [9.99995]  r  sin  (/>.„  -f  0°  1'  29") 

zo  =  [8.7722]  r  sin  (;.„  +  284°  35'  18"  +  0".027  d). 

Epoch  =  2405000th  day  of  the  Julian  Period  ==  1872,  July  25. 

/!o  =  /.  —  0".  13764  d, 

ico  =  [9.99929]  r  sin  (;.0  +  89°  58'  32"), 

ya  =  [9.99995]  r  sin  (A0  -f  0°  1'  28"), 

z0  =  [8.7722]  r  sin  (/>.0  -f-  284°  27'  53"  +  0".027  d). 

Epoch  =  2410000th  day  of  the  Julian  Period  =  1886,  Apr.  3. 

;.o  =/  —  0".  13765  d, 

x0  =  [9.99928]  r  sin  (i0  +  89°  58'  33"), 

?/0  =  [9.99995]  r  sin  (/>0  +  0°  1'  27") 

2o  =  [8.7723]  r  sin  (;.„  +  284°  20'  28"  -f  0".027  d). 

Epoch  =  2415000th  day  of  the  Julian  Period  =  1899,  Dec.  11. 

;.o  =  ;.  —  0".  13766  d, 

x0  =  [9.99928]  r  sin  (/>o  +  89°  58'  34"), 

y0  =  [9.99995]  r  sin  (A0  +  0°  1'  26") 

z0  =  [8.7723]  r  sin  (*0  +  284°  13'  3"  +  0".027  d). 

Epoch  =  2420000th  day  of  the  Julian  Period  =  1913,  Aug.  20. 

/o  =  /I  — 0".  13766  d, 
x0  =  [9.99928]  r  sin  (xo  -f  89°  58'  34"), 
ya  =  [9.99995]  r  sin  (/0  -f  0°  1'  24"), 
s0  =  [8.7723]  r  sin  (/,°  -4-  284°  5'  37"  -f-  0".027  d). 

8 


INTRODUCTION. 

In  the  above  expressions  nf  the  rectangular  coordinates,  (lie  logarithms  of  the  constant  factors,  inclosed  in  [I, 
li:i\e  been  given,  instead  of  tlie  constants  themseU es  ;  and  the  pertnrl>::tioiis  of  tin-  latitude  liave  lieen  neglected. 

Table  I.  contains  the  longitudes  of  tlie  principal  Observatories  from  Washington,  as  given  by  Dr.  GOULD  in 
the  American  Epheineris  for  1.S70.  West  longiludes  arc'  considered  as  positive. 

Tables  II.,  III.,  and  IV.  are  tables  of  Astronomical  Date's  in  mean  solar  days,  from  which  any  date,  given  in 
the  usual  form  of  reference  to  the  Christian  era.  may  be  reduced  to  its  value  in  days  and  decimals  of  a  day  of  the 
Julian  period.  They  are  taken  from  lYna  i.'s  Lunar  Tables.  l}\  adding  the  days  given  for  the  current  century 
to  the  days  of  the  previous  centennial  date,  we  obtain  the  number  of  days  elapsed  ot  the  Julian  Period  for  Jun.  0"' 
Mean  Noon  in  common  years  and  for  Jan.  I'1  in  bissextile  years.  To  this  should  be  added  the  days  and  decimals 
of  a  day  for  fractional  parts  of  a  year  given  in  Tables  111.  and  IV. 

Table  V.  contains  ihe  periods  of  the  various  argu nts,  and  multiplies  of  them,  which  it  is  sometimes  neces- 
sary to  subtract,  to  render  the  arguments  less  than  their  periods. 

Table  VI.  contains  for  Washington  Mean  Noon  of  Jan.  O'1  in  common  years,  Jan.  I'1  in  bissextile  years,  of 
each  year  from  1750  to  1950,  the  following  quantities  : 

L  =  -211°  IS'  1N".:W  —  On  17'  HV'.OO  4-  2106691".6218  / 

+  0".0001l:il  /-  4-  0".282  sin  (1  /•"  4-  3  /'  —  7  /"  4-  147°.l), 

the  hteger  i!>.  the  Arguments  I. — XIV.,  the  logarithm  of  the  sine  of  the  inclination,  and  the  supplement  to  360° 
of  the  mean  longitude  of  the  ascending  node.  The  term  0°  47'  40".00  in  L  is  equivalent  to  the  sum  of  all  the 
constants  which  have  been  added  to  the  quantities  in  the  tables  of  the  equation  of  the  centre,  and  of  the  periodic 
perturbations  of  the  orbit  longitude,  in  order  to  render  them  always  positive. 

Table  VII.  contains  for  every  day  of  the  year,  the  motion  of  the  mean  longitude,  and  the  motion  of  the  sup- 
plement of  the  node,  and  the  fraction  of  the  year  from  the  beginning  of  the  year. 

Table  VIII.  contains  the  motion  of  L  for  hours,  minutes  and  seconds;  also  for  tenths,  hundrcdths  and  thous- 
undihs  of  a  dav. 

Table  IX.  contains  the  factor  of  a  small  correction  to  be  applied  to  L,  on  account  of  the  inequality  of  its 
motion.  The  quantity  taken  from  this  table  must  be  multiplied  by  the  fraction  of  the  year  obtained  from  the 
preceding  table,  and  the  product  added  to  L. 

Table  X.  contains  the  lunation  of  the  Centre  for  every  tenth  of  a  day  of  Argument  I.  Its  secular  variation, 
corresponding  to  the  fractional  part  of  the  anomalistic  period,  is  included  in  the  numbers  of  the  table.  The  con- 
stant added,  to  render  all  the  numbers  positive,  is  47'  3".50. 

Tables  XI. — XXV.  contain  the  perturbations  of  the  Orbit  Longitude.  They  are  given  in  units  of  hundredths  of 
a  second  -of  arc. 

And  particularly, — Table  XI.  contains  the  factor  of  the  secular  perturbation  for  each  day  of  Argument  I.  The 
quantity  taken  from  this  table  must  be  multiplied  by  the  integer  ill.  The  logarithm  of  the  factor  is  also  given,  as 
some  may  prefer  making  the  multiplication  by  the  aid  of  logarithms. 

Table  XII.  contains  the  factor  of  that  part  of  the  secular  perturbation  which  varies  as  the  square  of  the  time. 
It  is  given  at  intervals  of  4  days  of  the  Argument  I.  The  quantity  taken  from  this  uible,  must  be  multiplied  by 
( i*1*/  •  'l'ne  l°garithm  of  the  factor  is  also  given.  The  formula  for  the  numbers  of  this  table  is 

4-  2.01  sin  M. 

Table  XIII.  contains  the  long  period  term,  due  to  the  action  of  the  Earth, 

4-  2".820  sin  (8  P  —  13  I"  -f  227°  58'). 

It  is  given  at  intervals  of  2  years  of  the  Argument  II.    The  constant  added  to  render  all  the  numbers  positive  is  2".82. 
Table  XIV.  contains  the  terms 

+  1".168  sin  (/  —  3  /'"  4-  117°  56') 
+  0".082  sin  (2  V  —  6  V"  +  74°.8) 

due  to  the  action  of  Mars.  They  are  given  at  intervals  of  200  days  of  the  Argument  III.  The  constant  added  is  1".  15. 
Table  XV.  contains  the  term 

4-  1".495  sin  (5  I"  —  3  f  4-  198°  24'), 

due  to  the  action  of  the  Earth.     It  is  given  at  intervals  of  40  days  of  the  Argument  IV.     The  constant  added  is  1".50 
•2  V  '•> 


INTRODUCTION. 


Fable  XVI.  contains  the  terms 

4-  3".515  sin  (2  /'  —  3  1"  +  268°  7'. 5) 
4-  0".188  sin  (4  /'  —  6  /"  +  340°.7), 

due  to  the  action  of  the  Earth.     They  are  given  at  intervals  of  16  days  in  the  Argument  V.     The  constant  added  is 
3".GO. 

Table  XVII.  contains  the  terms 


4.984  sin  (I'  —  /") 
-  11.489  sin  (2/'  —  2 /") 
4-    7.260  sin  (3  I'  —  3  I"  +  0°  7'.6) 
+     1.050  sin  (4  /'  —  4  /"  4-  0°.10') 
-|-    0.335  sin  (5  /'  —  5  /"  +  1°.5) 
4-    0.143  sin  (61'  —  G  I") 


ilur  in  the:  action  of  the  Earth. 
is  16".G.r). 

Table  XVIII  contains  the  term 


+  a067  sin  (  7  /'  —  7  I") 
4-  0.035  sin  (8  /'  —  8  /") 
4-  0.019  sin  (9  V  —  9  /") 
4-  0.013  sin  ( 10  V—  10  I") 
-\-  0.007  sin  (11  /'—  11  I") 
4-  0.004  sin  (12  V  —  12  /") 
4- 0.003  sin  (13d'—  13/"), 

They  arc  given  at  intervals  of  2  days  in  the  Argument  VI. 


The  constant  added 


4-  1".620  sin  (4  I'  —  5  I"  +  268°  24'.5), 

due  to  the  action  of  the  Earth.     It  is  given  at  intervals  of  4  days  in  the  Argument  VII.     The  constant  added  is  1".62. 
Table  XIX.  contains  the  term 

4-  0".657  sin  (2  /'  —  3  I'"  +  332°  44'), 
due:  to  the  action  of  Mars.     It  is  given  at  intervals  of  4  days  in  the  Argument  VIII.     The  constant  added  is  0".6fi. 


Table  XX.  contains  the  terms 


—  2".959  sin  (/'  —  /iv  4-  0°  31')  4-  0".041  sin  (3  /'  —  3  ZiT) 

4-  0".880  sin  (2  V  —  2  I")  4-  0".007  sin  (4  /'  —  4  I"), 

due  to  the  action  of  Jupiter.    They  are  given  at  intervals  of  2  days  in  the  Argument  IX.  The  constant  added  is  3". 35. 

Table  XXI.  contains  the  perturbations  due  to  the  action  of  Mercury.  The  formula  has  already  been  given  at 
page  3.  The  tabulation  is  to  double  entry,  the  horizontal  argument  being  L,  and  the  vertical  argument  X.,  which 
remains  constant  during  a  period  of  Argument  I.  When  Argument  I.  surpasses  the  limit  of  the  table,  224(1.7  should 
be  subtracted  from  it,  and  33.26  should  be  added  to  Argument  X.;  and  if  this  last  surpasses  60,  60  may  be  subtracted 
from  it.  The  constant  added  to  the  numbers,  to  render  them  positive,  is  0".85. 

Table  XXII.  contains  the  residual  perturbations  due  to  the  action  of  the  Earth.  The  analytical  expression  is 
that  given  on  page  3  with  the  omission  of  the  terms  which  have  been  tabulated  in  Tables  XIIL,  XV.,  XVI.,  XVII., 
and  XVIII.  The  tabulation  is  to  double  entry,  the  horizontal  argument  being  L,  and  the  vertical  argument  XL, 
which  remains  constant  during  a  period  of  Argument  I.  When  224d.7  is  subtracted  from  Argument  L,  147. (il 
should  be  added  to  Argument  XL;  and  if  this  last  exceeds  240,  240  may  be  subtracted  from  it.  The  constant 
added  to  the  numbers  of  this  table  is  1".40. 

Table  XXIII.  contains  the  residual  perturbations  due  to  the  action  of  Mars.  The  analytical  expression  is  that 
given  at  page  4,  with  the  omission  of  the  terms  which  have  been  tabulated  in  Tables  XIV.  and  XIX.  The  tabula- 
tion is  to  double  entry,  the  horizontal  argument  being  L,  and  the  vertical  argument  XII.,  which  remains  constant 
during  a  period  of  Argument  L  When  224d.7  is  subtracted  from  Argument  L,  19.6  must  be  added  to  Argument 
XII.;  and  if  this  last  exceeds  60,  60  may  be  subtracted  from  it.  The  constant  added  to  the  numbers  of  this  table  is 

Table  XXIV.  contains  the  residual  perturbations  due  to  the  action  of  Jupiter.  The  analytical  expression  is 
tint  given  at  page  4,  with  the  omission  of  the  terms  which  have  been  tabulated  in  Table  XX.  The  tabulation  is 
to  double  entry,  the  horizontal  argument  being  L,  and  the  vertical  argument  XIIL,  which  remains  constant  during  a 
period  of  Argument  I.  When  224d.7  is  subtracted  from  Argument  L,  3.11  must  be  added  to  Argument  XIIL;  and 
if  this  last  exceeds  60,  60  may  be  subtracted  from  it.  The  constant  added  to  the  numbers  of  this  table  is  2".35. 

Table  XXV.  contains  the  perturbations  due  to  the  action  of  Saturn.  The  analytical  expression  is  given  on 
page  4.  The  tabulation  is  to  double  entry,  the  horizontal  argument  being  L,  and  the  vertical  argument  XIV.,  which 


10 


I  NTIIODUCTION. 

remains  constant  during  a  period  of  Argument  I.      When  22  I'1. 7  is  subtracted  (V<ini  Argument  I..  O.S  inn  I  In-  added 
10    \  i  L'ument  XIV..  and  if  this  last  exceeds  ;{(i,  :j(i  may  lie  subtracted  from  it.      The  constant  added  Id  I 
of  this  talile  is  0".  10. 

The  preeedinic  tallies  give  the  t  )rhit   Longitude  of  Venus  referred  to  the  mean  eijuiimx  of  dale. 

TaMe  \\  \  I.  eonlains  the  eoiiiinon  logarithm  of  the  Elliptic  lladius  Vector,  for  every  lentil  of  a  da\  of  Argu- 
nent  I.  Its  secnlar  variation,  corresponding  In  the-  fractional  |iarl  of  the  anomalistic  period  is  included.  The 
formula  tabulated  is 

!).,S5!)31275  -  0.0000257  -  0.00297187  cos  M 
-  0.00001525  cos  -2  M  —  0.00000010  cos  3  M 

1'7  (<l'i!»iitity  from  Tab.  XXVII). 

The  term  0.0000'J.">7  is  equivalent  to  the  sum  of  all  the  constants,  which  have  been  added  in  the  tables  of  the  peri- 
odic perturbations,  in  order  to  render  the  numbers  al\va\s  positive. 

Tahles  XXVII.  X\XV.  contain  the  perturbations  of  log.  r;  they  are  given  uniformly  in  units  of  the  eighth 
decimal  ;  and  specially  : — 

Table  XXVII.  contains  (lie  factor  of  the  secular  perturbations  for  each  day  of  Argument  I.  The  quaniity 
taken  from  this  table  must  be  multiplied  by  the  integer  111.  The  logarithm  of  the  factor  is  also  given. 

Table  XXVIII  contains  the  factor  of  that  part  of  the  secular  perturbation  which  varies  as  the  square  of  the 
time.  It  is  given  for  intervals  of  1  days  in  the  Argument  I.  The  quantity  taken  from  this  table  must  be  multi- 


by  ( 


The  formula  for  the  numbers  of  this  table  is  —  2.1  cos  M. 


Table  XXIX.  contains  the  terms 

-  1N.6  —  23.0  cos  (6  I'  —  G  I") 
+  22S.2  eat  (/'  -  /")  -  11.5  cos  (7  /'  -  7  /") 
+  998.6  cos  (2  /'  -  2  /")  6.4  cos  (8  /'  —  8  /") 
_  H  11.8  cos  (li  /'  —  3  /"  +  0°  8')                                  3.5  cos  (9  /'  -  9  /") 

-  145.2  cos  (  1  /'  -  4  /")  2.6  cos  (10  /'  -  10  /"), 

-  52.2  cos  (5  I'  -  5  /"  +  0°  20') 

due  to  the  action  of  the  Earth.      The  constant  added  is  1594. 

Table  XXX.  contains  the  term 

+  162.2  cos  {4  f  —  5  /"  +  88°  52'), 
due  to  the  action  of  the  Earth.     The  constant  added  is  162. 

Table  XXXI.  contains  the  terms 

—     19.2  —  133.0  cos  (2  f  —  2  /iv) 

+  299.2  cos  (/'  -  /*  +  0°  20')  -      7.0  cos  (3  /'  -  3  /"), 

due  to  the  action  of  Jupiter.     The  constant  added  is  445. 

Table  XXXII.  contains  the  perturbations  due  to  the  action  of  Mercury.  The  formula  has  already  been  given 
on  page  4.  The  constant  added  is  34.  The  tabulation  is  to  double  entry,  and  the  remarks  which  have  been 
made  with  regard  to  Table  XXI.  also  apply  here. 

Table  XXXIII.  contains  the  residual  perturbations  due  to  the  action  of  the  Earth.  The  formula  is  that  given 
at  page'  1  with  the  omission  of  the  terms  which  have  been  tabulated  in  Tables  XXIX.  and  XXX.  The  constant 
added  is  150.  The  tabulation  is  to  double  entry,  and  the  remarks  made  with  regard  to  Table  XXII.  apply  here. 

Table  XXXIV.  contains  the  perturbations  due  to  the  action  of  Mars.  The  formula  has  been  given  at  page  5. 
The  constant  added  is  80.  The  tabulation  is  to  double  entry,  and  the  remarks  made  with  regard  to  Table  XXIII 
apply  here. 

Table  XXXV.  contains  the  residual  perturbations  due  to  the  action  of  Jupiter.  The  formula  is  that  given  on 
page  5,  when  the  terms  tabulated  in  Table  XXXI.  are  omitted.  The  constant  added  is  80.  The  tabulation  is  to 
double  entry,  and  the  remarks  made  with  regard  to  Table  XXIV.  apply  here. 

Table  XXXVI.  contains  the  perturbations  due  to  the  action  of  Saturn.     The  formula  has  been  given  at  pa-e  .">. 

11 


INTRODUCTION. 

The  constant  added  is  25.     The  tabulation  is  to  double  entry,  and  the  remarks  made  with  regard  to  Table  XXV 
apply  here. 

These  tables  (XX VI.— XXX VI.)  sutlicc  tor  finding  the  logarithm  of  the  radius  vector. 

Tables  \X\VII.  and  XXXVIII.  contain  the  perturbations  of  the  latitude  expressed  in  units  of  hundredths  of  a 
second  o!'  an-. 

Table  XXXVII.  contains  the  perturbations  due  to  the  action  of  the  Earth.  The  formula  has  been  given  at 
page  5.  The  constant  added  is  0".62.  The  tabulation  is  to  double  entry,  and  the  remarks  made  with  regard  to 
Table  XXII.  apply  here. 

Table  XXXVIII.  contains  the  perturbations  due  to  the  action  of  Jupiter.  The  formula  has  been  given  at  page 
5.  The  constant  added  is  0".21.  The  tabulation  is  to  double  entry,  and  the  remarks  made  with  regard  to  Table 
XXIV.  apply  here. 

The  latitude  of  Venus  is  then  obtained  in  the  following  way.     The  elliptic  latitude  is  obtained  from  the  formula 

log  sin  (elliptic  hit.)  =  log  sin  i  +  log  sin  [orbit  long.  +  (360°  —   ft)], 
in  which  the  orbit  longitude  is  corrected  for  perturbations.     Then  the  true  latitude  is  given  by  the  formula 

True  Latitude  =  Elliptic  Latitude  +  the  sum  of  the  quantities  derived  from  Tables  XXXVII.  and  XXXVIII.  —  0"83.* 

Table  XXXIX.  contains,  for  the  beginning  of  each  year  between  1750 — 1950,  the  values  of  the  quantities  KIt 
Ky,  K2,  log  /tx,  log  /.-,.,  log  k.,.  and  the  Arguments  XV.  and  XVI.  on  which  depend  respectively  the  lunar  and  solar 
nutation. 

The  beginning  of  the  year  for  Arguments  XV.  and  XVI.  must  be  understood  as  being  the  Washington  mean 
noon  of  Jan.  0,  (Jan.  1  in  bissextile  years,).  But  the  other  six  quantities  of  this  Table  are  given  for  this  time  of  the 
beginning  of  the  year  only  for  1850,  and  backwards  and  forwards  from  this  epoch  they  proceed  by  intervals  of  a 
tropical  year.  This  modification  has  been  made,  in  order  that  the  motion  of  these  quantities  for  the  fractional 
part  of  the  year  might  be  included  in  Table  XLI.  From  each  of  the  quantities  /(Tx,  Ky,  and  K%,  there  has  brrn 
subtracted  the  constant  20".00,  and  from  log  £y  the  constant  0.0000089,  and  from  log  kt  the  constant  0.0000560. 
These  constants  are  equivalent,  in  each  case,  to  the  sum  of  the  constants  which  have  been  added  to  the  quantities 
in  Tables  XL.  and  XLI.  to  render  them  positive.  Moreover  to  K^  has  been  added  the  small  correction,  due  to 
lunar  nutation,  over  and  above  the  lunar  nutation  itself;  and  to  log  fcx  has  been  added  the  small  correction  due  to 
lunar  nutation. 

Table  XL.  contains  the  variations  of  the  quantities  K^,  Ky,  Kz,  log  fcy,  and  log  k7l  which  are  produced  by  lunar 
nutation.  The  two  last  arc  expressed  in  units  of  the  seventh  decimal  place.  These  quantities  have  all  been  com- 
puted for  the  epoch  1850,  and  are  subject  to  small  secular  changes,  which,  except  in  the  case  of  the  correction  of 
Kx,  arc  barely  sensible  in  the  course  of  a  century.  The  variation  of  A  K2  in  a  century  has  therefore  been  given 
in  the  adjacent  column. 

The  constants  which  have  been  added  to  render  the  numbers  positive,  are  18".00  to  A  K±,  18". 00  to  A  Ky, 
17".00  to  A  Kz,  88  units  to  J  log  iy,  430  units  to  J  log  k,..  The  lunar  nutation  of  the  equinox  can  be  obtained 
from  the  value  of  A  K%  by  subtracting  18".00.  The  formulae  for  the  quantities  tabulated  arc 

A  KK  =  18".00  +  A  </>, 
A  Ky  =  18".00  +  1.0044  A  {•  +  0.0690  A  E, 
A  K,  =  17".00  +  0.9498  A  <,'•  +  0.3323  A  e, 
sec.  var.  of  A  K,,  =  +  0.0030  A  3, 

A  log  ky  =    88  +  0.5469  A  f  -  9.480  A  e, 
J  log  kt  =  430  —  2.534    A  <J>  +  45.71  J  E, 

when  for  A  $  and  J  E  are  substituted  those  parts  of  the  values  of  these  quantities  given  on  page  6  which  depend 
on  £1  ([ .     The  part  of  A  K^  which  has  been  applied  to  K^  in  Table  XXXIX  is 

+  0.0015  J  v\ 

untl  tne  value  of  J  log  fcx  which  has  been  added  to  i-x  in  the  same  Table  is 

-  0.0181  J  </'. 

"The  single  term  in  the  perturbations  of  the  latitude,  due  to  the  action  of  Saturn,  has  not  II.HMI  tabulated.  It  seemed  super, 
fluous  to  take  account  of  it,  when  the  corresponding  term  in  the  latitude  of  the  Kartli,  producing,  at  maximum,  an  effect  in  the 
geocentric  position  of  Venus,  nearly  three  times  greater,  is  neglected  by  llansen  and  Olufsen  in  their  "  Tables  du  Soldi." 

12 


INTRODUCTION. 

Table  XL  I.  contains  the  variations  of  the  quantities  A'  .  A\ ,  A".,  K,Lr  /-^  -,111]  log  /.-.  \vhicli  arc  produced  by 
solar  nutation.  augmented  hy  the  niolioii  oi'tlie  quantities  in  the  tVac-tional  part  of  the  tropical  year.  J  log  /. 
J  loir  l;f  are  expressed  in  units  of  the  seventh  decimal  place.  The  quantities  have  been  computed  t'ur  the  epoch 
1  >.">(>.  The  secular  variation  J  A',,  becoming  sensible  ill  the  course  of  a  eentur\  ,  is  given  in  the  adjacent  column. 
The  last  column  contains  the  solar  nutation  of  the  equinox.  The  constants  which  have  been  added  are  2".00  to 
J  A.,  ^".00  to  J  A"v,  ;}".00to  J  A',.,  1  unit  to  J  log  t,,  and  130  units  to  J  log  /.-,.  The  formula1  lor  the  quantities 
tabulated  are, 

J  A'v  =  2".00  +  0".05    r  +  J  v\ 

j  A',  =  •->".(>(>  4-  0".12G  r  +  J  ,,'•  4-  0".03N  sin  (2  O  +  98°.2), 
J  K7.  =  3".00  -  l".H(il  r  4-  J  v'>  4-  0". lift  sili  (2  O  +  71°.0), 
sec.  var.  J  A'2  =  +  0".049  -, 

J  log  /tv  =  1  4-  22.145  r  4-  5.3  sin  (2  O  +  263°.5), 

J  log  /.-,  =  130  -  103.110  -  4-  25.  1  sin  (•>  O  +  N33.8), 

r  denoting  tlie  fraction  of  the  year,  and  the  value  of  J  <,'•  being 

-   1".254  sin  2  Q. 

The  proper  values  of  A'x,  A'y  &c.,  needed  for  computing  the  values  of  .r,  //,  anil  z  referred  to  the  true  equinox 
and  equator  of  date,  are  therefore  obtained,  by  adding  the  quantities  obtained  from  Tables  XL.  and  XLI.  to  the 
quantities  given  in  Table  XXXIX.  for  th<;,be«iiinin<!!  of  the  i/car.  And  there  is  no  need  of  interpolation  in  this 
laM  Table,  except  for  log.  A\,  which  however  is  nearly  constant. 

Table  XLI  1.  contains  the  values  of  the  factors  by  which  the  perturbation  of  the  latitude,  obtairrcd  from  Tables 
XXXVI.I.  and  XXXVIII.  by  subtracting  0".83,  and  expressed  in  hundredths  of  a  second  of  arc,  must  be  multi- 
plied, in  order  to  obtain  the  corresponding  corrections  of  the  coordinates  a;,  y,  and  z  expressed  in  units  of  the  seventh 
decimal  place.  The  Argument  is  the  Orbit  Longitude. 

Table  XLI  1 1.  contains  the  1'arallax  and  Seinidiameter.  The  Argument  is  the  logarithm  of  the  planet's 
distance  from  the  Earth.  The  formula?  have  already  been  given  at  page  8.  The  value  of  the  semidiameter  here 
given  lias  still  need  to  be  increased  by  a  constant  quantity  for  the  effect  of  irradiation,  but  varying  for  different 
observers  and  instruments,  when  the  reduction  ot  observations  is  in  question. 

Tables  XLIY.  and  XLV.  give  Ihe  means  of  obtaining  the  mean  longitude  and  arguments  for  a  time  not  con- 
tained between  the  limits  1750 — 1950. 

Table  XLIV.  contains  the  quantities  which  must  be  added  to  the  quantities  of  the  19th  century  contained  in 
Tables  VI.  and  XXXIX.,  to  obtain  the  mean  longitude  and  arguments  for  the  beginning  of  the  corresponding 
year  of  any  other  century  between  300  B.  C.  and  2300  A.  D.  The  numbers  in  the  columns  headed  I' —  50,  must 
lie  multiplied  by  (f  —  50),  t'  denoting  the  number  of  years  from  the  beginning  of  the  century,  and  the  products 
added  to  the  numbers  of  the  preceding  column.  In  the  case  of  log  sin  i,  the  numbers  of  the  column  headed 
I'  —  50  must  be  understood  as  being  in  units  of  the  last  decimal  place  of  log  sin  i.  In  using  this  Table  for  dates 
which  are  B.  C.  the  given  year  must  be  conceived  as  increased  algebraically  by  a  unit.  It  will  be  noticed  that 
two  lines  occur  for  the  argument  1500:  the  first  is  for  dates  which  are  according  to  the  Julian  calendar  (Old 
Style),  and  the  second  Tor  those  which  are  according  to  the  Gregorian  calendar  (New  Style).  The  Julian  calendar 
ends  with  Oct.  4,  1582  ;  and  the  Gregorian  begins  with  Oct.  15,  1582. 

Table  XLV.  contains  the  values  of  the  inequality  of  the  longitude  to  long  period, 

4-  0".282  sin  (4  V"  —  7  I"  +  3  V  4-  147°.  1), 

and  of  certain  multiples  of  the  period  of  the  argument  in  years.  As  this  inequality  has  been  added  to  the  numbers 
of  the  column  headed  L  in  Table  VI.,  we  must  enter  the  Table  first  with  the  argument  equal  to  the  corresponding 
year  of  the  19"'  century  and  take  the  equation  with  the  opposite  sign ;  and  next  with  the  argument  equal  to  the  year 
of  the  given  date,  and  take  the  corresponding  equation:  then  both  these  quantities  must  be  added  to  the  L  resulting 
from  the  previous  Tables.  If  the  year  of  the  given  date  is  not  found  in  the  limits  of  this  Table,  that  multiple  of 
the  period  of  the  argument,  which  is  requisite,  must  be  added  to  it  or  subtracted  from  it. 

Table  XLVI.  contains  the  Reduction  of  the  Orbit  Longitude  to  the  ecliptic.  The  Argument  is  the  "Orbit 
Longitude  4-  360°  —  ft",  or  this  angle  diminished  by  180°  when  it  exceeds  180°.  It  is  given  for  every  10'  of  the 

13 


INTRODUCTION. 

Argument.     The  arrangement  of  the  Table  will   be  easily   understood.     The  Table  is  constructed  for  the  epoch 
lsr,0.(),  and  the  variation  in  a  century,  of  the  numbers  tabulated,  is  given   in  the   last  column  but  one,  for  every 
ee.      The  1'imnilii  for  the  reduction  to  the  ecliptic  is 

—  ISO".!)  It  sin  2  (I  +  360°  —  ft)  +  0".079  sin  4  (A  +  360°  —  &), 

and  for  its  secular  variation 

-  0".113  sin  -2  (/-  +  360°  -  a). 


DIRECTIONS  FOR  THE  USE  OF  THE  TABLES. 

The  given  time  must  be  reduced  to  Washington  Mean  Time  by  the  aid  of  Table  I.  The  hours,  minutes  and 
see, ,11,1s  can  then  lie  reduced  to  the  equivalent  decimal  part  of  a  day  by  Table  IV.;  and  the  whole  number  of  clays 
which  have  elapsed  since  the  beginning  of  the  year  can  be  found  from  Table  III. 

The  values  of  the  mean  longitude  L,  m  and  the  fourteen  arguments  of  the  perturbations  are  taken  from  Table 
VI.  for  the  given  year,  if  it  lies  between  1750  and  1949.  If  we  do  not  want  the  heliocentric  longitude  and  latitude 
of  the  planet,  but  intend  to  compute  the  geocentric  coordinates  by  the  Gaussian  process,  the  quantities,  in  the 
columns  of  this  Table,  headed  Log.  sin  i  and  360°  —  & ,  will  not  be  needed. 

From  Table  VII.  will  be  obtained  the  motion  of  L  from  the  beginning  of  the  year  to  the  given  day;  and  also 
the  fraction  gf^he  year;  from  Table  IX.  the  factor  which  must  be  multiplied  by  the  fraction  of  the  year  and  the 
product  added  to  L ;  and  from  Table  VIII.  the  motion  of  L  for  hours,  minutes  and  seconds,  or  for  decimal  parts  of 
a  day.  The  quantities  obtained  from  Tables  VII. — IX.  being  added  to  the  L  from  Table  VI.,  we  obtain  the  tabular 
mean  longitude  of  the  planet  for  the  given  date. 

To  Arguments  I. — IX.,  II.  excepted,  we  add  the  number  of  days  and  decimal  part  of  a  day  which  have 
elapsed  since  the  beginning  of  the  year ;  to  Argument  II.  we  add  the  fractional  part  of  the  year.  If  any  argument 
thus  obtained,  exceed  its  period  given  in  Table  V.,  we  subtract  as  many  multiples  of  the  period  as  may  be  neces- 
sary to  reduce  il  below  its  period.  To  the  Argument  in,  we  add  as  many  units,  as  we  have  subtracted  multiples 
of  its  period  from  Argument  I.,  and  to  Arguments  X. — XIV.  we  add  severally  the  same  number  of  multiples 
of  the  numbers  33.26,  147.64,  19.6,  3.11,  and  0.8.  The  values  of  these  multiples  are  given  in  Table  V.  If  any 
Argument  X. — XIV.  exceed  its  period  given  in  Table  V.,  we  may  subtract  from  it  the  largest  contained  multiple 
of  its  period. 

The  Equation  of  the  Centre  is  obtained  from  Table  X.  with  the  Argument  I.  The  perturbations  of  the  longi- 
tude in  hundrcdlhs  of  a  second  of  arc  will  be  obtained  with  the  proper  arguments  from  Tables  XI. — XXV- 
The  number  obtained  from  Table  XI.  must  be  multiplied  by  the  integer  m,  and  the  number  from  Table  XII.  by 

.         -2 

the  factor  |  m  )  ;'the  logarithms  of  the  numbers  in  these  two  tables  have  also  been  given  in  the  adjacent  column, 

in  order  that,  if  preferred,  the  multiplication  may  be  performed  by  their  aid.  The  Equation  of  the  Centre  and 
these  perturbations  being  added  to  the  mean  longitude,  we  obtain  the  orbit  longitude  referred  to  the  mean  equinox 
of  date. 

The  Logarithm  of  the  Elliptic  Radius  Vector  is  obtained  from  Table  XXVI.  with  the  Argument  I ;  and  its 
perturbations,  in  units  of  the  eighth  decimal,  with  the  proper  arguments  from  Tables  XXVII. — XXXVI.  The 
number  obtained  from  Table  XXVII.  must  be  multiplied  by  the  integer  us,  and  the  number  from  Table  XXVIII. 

by  the  factor  ( .VJY  !  tnc  logarithm  of  the  number  is  also  given  in  Table  XXVII.,  in  order  that,  if  preferred,  the 

multiplication  may  be  performed  by  its  aid.  If  the  sum  of  the  numbers  thus  obtained  from  Tables  XXV1I.-XXXVI. 
be  divided  by  10,  and  the  quotient  be  added  to  the  last  figures  of  the  quantity  obtained  from  Table  XXVI.,  we  shall 
have  the  common  logarithm  of  the  radius  vector  of  the  planet. 

If  we  diminish  by  83  the  sum  of  the  numbers,  obtained  from  Tables  XXXVII.  and  XXXVIII.  with  the  proper 
arguments,  we  shall  have,  in  hundredths  of  a  second  of  arc,  the  perturbations  of  the  latitude. 

The  values  of  7ix,  Ks,  &c.,  and  Arguments  XV.  and  XVI.  arc  to  be  taken  from  Table  XXXIX.  for  the 
given  year.  And  to  Arguments  XV.  and  XVI.  should  be  added  the  number  of  days  and  the  decimal  part  of  a  day 
elapsed  since  the  beginning  of  the  year  ;  and  if  Argument  XV.  exceed  its  period,  given  in  Table  V.,  the  period 

14 


1  NTRODUGTION. 

should  !><•  subtracted  from  it.  The  corrections  of'  A  .  /v"  .  &c.,  arc  obtained  from  Tables  X  I,,  and  XLI.,  with  the 
respective  Arguments  XV.  and  XVI.  In  the  ease  of  K,  in  carl.  Table,  the  variation  in  100  years,  given  in  the 
adjacent  column,  must  be  taken  into  account;  we  multiply  it  by  the  fractional  part  of  the  eentur\  elapsed  since 
L850,  and  add  the  product  to  the  quantity  obtained  from  the  preceding  column.  T  nations  being  added 

to  the-  values  of  A"..  A".,  &C.,  obtained  iritlwut  iiitff  illation  from  Table  XXXIX.,  we  have  the  proper  values  of 
these'  quantities  for  computing  the  rectangular  coordinates  of  the  planet  referred  to  the  true  equinox  and  equator 
of  date. 

It'  r  denote  the  radius  vector,  and  /  the  orbit    longitude   of  the  planet,  these  coordinates  are  obtained  by  the 

formula' 

x  =  i'x  r  sin  ().  +  K^), 

y  =  k,.  r  sin  (/.  -f-   A"y), 

;    =  /,',  /•  sill  (/    +    K,  ). 

The  values  of  the  coordinates  thus  found  need  correction  for  the  effect  of  perturbations  in  latitude.  To 
obtain  these  corrections  we  multiply  the  perturbations  of  the  latitude,  expressed  in  hundredlhs  of  a  second  of  arc, 
respectively  by  the  three  factors  obtained  from  Table  XI,  11.  with  the  argument  /.,  and  the  products  are  the  respec- 
tive corrections  of  the  coordinates  expressed  in  units  of  the  seventh  decimal. 

If  A",  V'and  Z  denote  the  coordinates  of  the  Sun  referred  to  the  same  system  of  planes  as  j  ,  i/  and  z,  the- 
atric right  ascension  a,  declination  »,  and  distance  from  the  Earth  J,  of  the  planet,  are  obtained  from  the 
equations, 

J  cos  a.  cos  <5  =  x  +  -Y, 
A  sin  a.  cos  ft  =  y  +  Y, 

J  sin  •»  =  2  +   Z. 

The  '/  and  <t  thus  obtained  have  still  to  be  corrected  for  aberration,  if  we  desire'  the  apparent  position  of  the 
planet.  The  aberration  time  T  in  days  is  given  by  the  equation 

log  T  =  7.7(J052  +  log  J  ;  or,  T  =  .005761  J. 

If  '       ami  '       denote  the  daily  variation  of  a  and  o  at  the  given  date,  the  corrections  for  aberration  are 

/I  I  d  t 

.  rpd  a 

J,_-T_, 


Finally,  from  Table  XLIII.,  we  can  obtain,  with  the  argument  log  J,  the  parallax  and  scmidiameter  of  the 
planet. 

If  we  desire  to  have  the  heliocentric  longitude  and  latitude,  we  take  from  Table  VI.  the  values  of  log.  sin  i 
and  :J60°  —  Q  for  the  given  year.  The  motion  of  360°  —  Q,  for  the  fraction  of  the  year  is  given  in  Table  VII.; 
that  of  log  sin  i  can  readily  be  inferred  from  Table  VI.  Then  if  the  latitude  be  computed  from  the  equation, 

log  sin  lat.  =  log  sin  i  +  log  sin  (A  +  360°  —  $)» 

and  the  perturbations  of  the  latitude,  which  have  already  been  obtained,  be  added  to  it,  we  shall  have  the  helio- 
centric latitude  required.  The  ecliptic  heliocentric  longitude,  referred  to  the  mean  equinox  of  date,  will  be  got  by 
adding  to  /.  the  reduction  to  the  ecliptic,  from  Table  XLVI.  As  the  value  of  the  reduction,  given  in  the  body  of  the 
Table,  is  for  the  epoch  1850,  we  must  apply  to  it  the  variation  in  100  years  multiplied  by  the  fraction  of  a  century 
elapsed  since  1850.  The  heliocentric  longitude  referred  to  the  true  equinox  of  date  will  be  found  by  adding  the 
nutation  of  the  equinoxes  in  longitude.  The  lunar  nutation  will  be  obtained  by  subtracting  18"  from  J  A\  in 
Table  XL.;  the  solar  nutation  is  given  in  the  last  column  of  Table  XLI. 
x,  y,  and  z  may  then  be  obtained  by  the  formulae 

x  =  r  cos  /  cos  V 

y  =  r  cos  /  sin  //  cos  e'  —  r  sin  /  sin  e' 

~  =  r  cos  /  sin  /'  sin  3'  +  ;•  sin  /  cos  c' 

in  which  /'  and  /  are  the  heliocentric  longitude  anil  latitude,  and  e'  =  £  -f  J  £,  the  apparent  obliquity  of  the  ecliptic. 

15 


INTRODUCTION. 

If  the  given  year  is  not  between  the  limits  1750—1949,  we  take  from  Tables  VI.  and  XXXIX,  the  values 
of  L,  m,  the  Arguments  1.— XVI.,  log  sin  i  and  360°  -  £,  for  the  corresponding  year  of  the  19th  century, 
(remembering  to  add  algebraically  a  unit  to  the  year  if  the  given  date  is  before  the  Christian  era.) 

We  add  to  these  the  quantities  obtained  from  Table  XLIV.,  with  the  given  century  as  the  Argument.  More- 
over we  add  to  L,  I,  log  sin  i  and  360°  —  Q  respectively  the  quantities  given  in  the  adjacent  columns,  headed 
I'  —  50,  multiplied  by  this  factor,  (I'  denoting  the  number  of  years  of  the  given  century,)  noticing  that  in  the  case 
of  log  sin  i,  the  quantities  in  the  column  headed  I'  —  50  are  in  units  of  the  last  decimal  of  this  quantity.  It  will  be 
observed  that  the  argument  1500  occurs  twice  in  Table  XLIV.;  the  first  line  is  to  be  employed  for  dates  in  old 
style,  the  second  for  dates  in  new  style. 

After  this,  we  proceed  precisely  as  before,  except  that  Table  VIII.  not  being  available,  we  employ  in  its  stead 
Table  XLV.,  which  we  enter  twice,  first  with  the  corresponding  year  of  the  19th  century  as  the  argument,  and 
subtracting  from  L  the  equation  obtained;  next  with  the  given  year,  as  the  argument,  or  this  augmented  or  dimin- 
ished by  the  requisite  number  of  multiples  of  the  period,  which  will  be  found  at  the  bottom  of  the  Table ;  and 
adding  to  L  the  equation  thus  obtained. 

In  this  case,  we  must  necessarily  deduce  the  heliocentric  longitude  and  latitude  of  the  planet,  since  the  tables 
for  finding  7fx,  A',.,  &c.,  arc  restricted  to  the  years  1750 — 1949.  The  method  of  computing  by  rectangular  coor- 
dinates is  only  to  be  preferred  when  we  have  the  coordinates  of  the  sun  ready  at  hand. 

In  computing  an  ephemeris  we  shall  avoid  the  horizontal  interpolation  in  the  tables  to  double  entry,  if,  instead 
of  computing  the  perturbations,  for  the  Washington  Mean  Noon  of  some  particular  day,  and  for  equal  intervals 
thereafter,  we  compute  the  value  of  the  perturbations,  for  the  times,  when  Arg.  I.  is  an  exact  multiple  of  8  days, 
and  then  the  interpolation,  with  reference  to  Arg.  I.,  can  be  performed  on  the  sums.  It  will  be  found  that  the 
interval  of  8  days  is  not  too  long  for  the  secure  interpolation  of  intermediate  values.  However,  if  m  should  be 
quite  large,  that  is,  if  the  given  time  is  quite  distant  from  1850,  the  terms  of  the  perturbations,  which  involve  this 
factor,  may  be  computed  separately,  for  the  times,  for  which,  the  ephemeris  is  wanted.  In  all  cases,  the  interpola- 
tion of  the  sums  of  the  perturbations,  to  the  times  of  the  ephemeris,  will  be  easier,  if  these  sums  are  first  interpolated 
into  the  middle,  that  is,  for  every  4  days.  In  the  computation  of  an  isolated  position  even,  this  method  of  obtaining 
the  perturbations,  first  for  the  times  when  Arg.  I.  is  a  multiple  of  8  days,  can  bo  followed  with  advantage,  at  least 
as  far  as  regards  the  tables  to  double  entry. 


The  following  examples  will  sufficiently  illustrate  the  foregoing  precepts: — 

1.  Required  an  ephemeris  of  the  heliocentric  position  of  Venus,  for  Washington  Mean  Noon,  at  intervals  of  2 
days,  and  covering  the  time  of  the  Transit  on  Dec.  8th,  1874. 

We  will  commence  the  calculation  of  the  perturbations  at  310d.3195  from  the  beginning  of  the  year  =  Nov. 
6a.3195,  when  the  value  of  Argument  I.  is  160d. 

Preparation  of  the  Arguments. 


Table  VI.,  1874, 
Day  of  Year, 
Table  V.,  Periods, 

Arguments  for  Date, 

No.  of  days  to  end  of  period 

Table  V.,  Periods, 


Ill 

I. 

II. 

HI. 

IV. 

V. 

VI. 

VII. 

VIII. 

IX. 

39 

74.3513 

19L9 

8583 

d 

346 

d 

798.5 

24L22 

d 
92.5 

129.8 

d 

52.83 

310.3495 

0.8 

310 

310 

310.3 

310.35 

310.3 

310.3 

310.35 

1 

-224.7008 

-243.2 

-220.6 

-236.99 

40 

160.0000 

192.7 

8893 

656 

1108.8 

551.57 

159-.6 

219.5 

126.19 

eric 

id 

40.00 

8.0 

-583.92 

—220.6 

7.65 


6.9 


16 


INTRODUCTION. 

X.  M  XII.  XIII 


XIV. 


XV. 


XVI. 


42.20 

17.72            53.0 

27.03 

30.6 

6005.2 

d 
1.8 

:{:!.v!ti 

147.(il             19.6 

3.11 

0.7 

310.0 

310.0 

-60.00 

-60.0 

Table  VI..  iv;  I, 

Table  V.,  Incr.  of  in  =  1, 

Periods, 

Arguments  for  Date,  15.46  165.36  12.6  301.4  31.3 

Perturbations  of  the    Lon<fitii<!i',   in   Iniml ri'iltlis  of  a  srcontl. 


6315.2         311.8 


Arg.  I. 

160 

l<i:s 

176 

181 

192 

200 

208 

216 

221 

Table  XI      .... 

+  491 

+  507 

+  198 

+4(>  I 

+406 

+  328 

+282 

+  121 

+  10 

Table.  XIII         .      .      . 

188 

187 

187 

187 

187 

187 

187 

187 

186 

Table  XIV    .      .      .      . 

157 

157 

157 

158 

158 

159 

156 

159 

160 

XV     .... 

128 

126 

128 

181 

134 

136 

188 

141 

144 

Table  XVI   .... 

847 

834 

821 

308 

•Jill 

281 

266 

255 

242 

Table  XVII       .     .     . 

1793 

1708 

1665 

1656 

1667 

1679 

1672 

1631 

1548 

Table  XV11I      .      .      . 

2GO 

231 

200 

167 

134 

101 

72 

46 

25 

Table  XIX  .... 

0 

1 

5 

12 

22 

34 

48 

62 

77 

Table  XX      .... 

431 

519 

591 

642 

668 

670 

650 

612 

563 

Table  XXI   .     .     .     . 

22 

28 

25 

27 

29 

31 

31 

39 

44 

Table  XXI  I       .     .     . 

189 

138 

139 

141 

113 

145 

145 

141 

135 

Table  XXIII     .     .     . 

34 

23 

22 

20 

18 

16 

18 

12 

10 

Table  XX  IV      .      .      . 

2:>  i 

244 

234 

225 

219 

216 

216 

218 

222 

Table  XXV        .      .      . 

36 

33 

82 

82 

:u 

36 

40 

45 

51 

Sums      .... 

1205 

4231 

4204 

4170 

4113 

4019 

3875 

3672 

3417 

\>ii. — Tlie   inequality   from   Table   XII.   is  insensible  at  tins  epoch,  as  is  also  the   corresponding   one  of  Log.   r  in 
Table    -\\VII1 

Perturbations  of  Log  r,  in  units  of  the  eighth  decimal. 


Arg.  I. 

160 

168 

176 

184 

192 

200 

208 

216 

224 

Table  XXVII  .     .     . 

-133 

-15 

+  104 

+219 

+323 

+411 

+478 

+  522 

+  538 

Table  XX  IX      .      .      . 

2146 

1989 

1850 

1753 

1716 

1748 

1841 

1978 

2136 

Table  XXX        .      .      . 

292 

309 

320 

321 

321 

311 

295 

274 

248 

Table  XXXI     .     .     . 

17 

66 

141 

236 

339 

440 

528 

594 

636 

Table  XXXII  .     .     . 

50 

46 

36 

24 

13 

9 

9 

12 

11 

Table   XXXIII        .       . 

231 

221 

214 

210 

211 

216 

224 

235 

245 

Table  XXXIV       .     . 

85 

70 

57 

46 

36 

29 

23 

20 

19 

Table  XXXV    .      .      . 

140 

184 

125 

112 

99 

85 

73 

65 

60 

Table  XXXVI      .     . 

36 

32 

27 

22 

17 

11 

6 

3 

0 

Sums     .... 

2864 

2852 

2874 

2946 

3075 

3260 

3177 

3703 

3893 

Perturbations  of  the  Latitude,  in  hundrcdths  of  a  second. 


Arg.  I. 

160 

168 

176 

184 

192 

200 

208 

216 

224 

Table  XXXVII     . 
Table  XXX  VI  11   .     . 
Constant  

39 
34 

—  83 

43 
35 

—  S3 

46 
36 

—  83 

53 
36 

—83 

59 
35 

83 

65 
34 

83 

71 
82 

—83 

76 
30 

—  83 

80 

27 

—83 

Sums     .... 

-10 

—  5 

-    1 

+  6 

+  11 

+  16 

+20 

+23 

+24 

17 


INTRODUCTION. 

Interpolating  the  perturbations  of  the  longitude  and  log  r  to  intervals  of  4  days,  we  have, 


Arg.  I. 

I'm.  of  the 
Long. 

uiir. 

Pert    of 
Log  r. 

Diff. 

Arg. 

Pert,  of  the 
Long. 

Diff. 

Pert,  of 

Log,. 

Diff. 

d 

d 

it 

160 
164 

168 
172 
176 
180 
184 
188 
192 

42.65 

12.  17 

42.31 

42.18 
42.04 
41.89 

41.70 
41.45 
41.18 

—  18 
1C 

13 

14 
15 
19 
95 

—  :V2 

2864 

2855 
2852 
2858 
2874 
2903 
2946 
3003 
3075 

—  9 
—   3 
+   G 
16 

89 

43 

57 

+  72 

192 
196 
200 
204 
208 
212 
216 
220 
221 

41.13 
40.72 
40.19 
39.51 
38.75 
37.80 
36.72 
35.50 
34.17 

—   41 
53 
05 
79 
95 
108 
139 
—  133 

3075 
3162 
3260 
3365 
3477 
3592 
3703 
3804 
3893 

+   87 
98 
105 
112 
115 
111 
101 
+  89 

The   Orbit  Loin'Jludc  and  Log.  r.     Washington  Mean  Noon. 


Date. 

Sloan  Longitude 

Eqtia.  of  the 

Pert,  of 

Log.  Elliptic  r 

Pert,  of 

Arg.  I. 

from  Tablrs 

Centre  from 

the  Long. 

Orbit  Long. 

from  Table 

Log.  r. 

Log.  /•. 

1-71. 

VI.-VIII. 

Table  X. 

XXVI. 

Dec.   3 

d 

337 

186'.6505 

0            1             II 

68    3     8.37 

5  45J20 

it 

41.54 

a       i       a 

68     9  35.11 

9.8578827 

298 

9.8579125 

5 

339 

188.6505 

71   15  23.98 

7     5.00 

41.40 

71  23  10.38 

9.8577382 

301 

9.85776H3 

7 

341 

190.6505 

74  27  39.59 

8  32.38 

41.24 

74  36  53.21 

9.8575986 

305 

9.8576291 

9 

313 

192.6505 

77  39  55.21 

10    7.11 

41.07 

77  50  43.39 

9.8574644 

309 

9.8574953 

11 

345 

194.6505 

80  52  10.82 

11  48.87 

40.87 

81     4  40.56 

9.8573358 

313 

9.8573671 

13 

347 

196.6505 

84    4  26.44 

13  37.36 

40.64 

84   18  44.44 

9.8572135 

318 

9.8572  153 

Inequalities  of  7tx,  Ky,  fyc. 


4E*. 

AK,. 

4Jk 

A  log  kr 

I):iv  of 

Year. 

Table 

Table 

Sum. 

Table 

Table 

Sum. 

Table 

Table 

Sum. 

Table 

Table 

Sum. 

XL. 

XLI. 

XL. 

XLI. 

XL. 

XLI. 

XL. 

XLI. 

d 

310 

KX68 

it 
0.78 

// 

11.46 

// 

11.23 

if 
0.83 

12!o6 

// 

12.81 

a 
0.24 

13!05 

5 

19 

24 

320 

10.82 

0.85 

11.67 

11.37 

0.90 

12.27 

12.96 

0.19 

13.15 

5 

21 

26 

330 

10.96 

1.07 

12.03 

11.52 

1.11 

12.63 

13.11 

0.28 

13.39 

5 

23 

28 

310 

11.11 

1.39 

12.50 

11.66 

1.42 

13.08 

13.26 

0.49 

13.75 

4 

25 

29 

350 

11.25 

1.80 

13.05 

11.81 

1.83 

18.64 

13.10 

0.80 

14.20 

4 

27 

31 

360 

11.40 

2.26 

13.66 

11.95 

2.30 

14.25 

13.55 

1.19 

14.74 

4 

28 

32 

370 

11.54 

2.68 

14.22 

12.10 

2.72 

14.82 

13.70 

1.57 

15.27 

3 

28 

31 

J  log  Arz. 

Day  of 
Year 

^x- 

Er 

K* 

Log  £x. 

Log  ky. 

Log  i-z. 

Table 

Table 

Sum. 

XL. 

XLI. 

<1 
310 

828 

46 

874 

89°  58  23.90 

o    /    // 

1  27  22.22 

352°  44'  25.01 

9.9992854 

9.9598380 

9.6179435 

320 

829 

34 

863 

24.11 

22.43 

25.11 

4 

82 

424 

3.'5() 

830 

23 

853 

24.47 

22.79 

25.35 

4 

84 

414 

310 

831 

14 

845 

24.94 

23.24 

25.71 

4 

85 

406 

350 

833 

7 

840 

25.49 

23.80 

26.16 

4 

87 

401 

360 

834 

3 

837 

26.10 

24.41 

26.70 

4 

88 

398 

370 

835 

2 

837 

26.66 

24.98 

27.23 

4 

87 

398 

18 


INTRODUCTION. 


<\>mj»ilii:'iiin   «!'  /lie    Ri-r/fiiiHiilnr   Co'i'irili 


Dai.-,  1-71 

/.  +  K, 

a  +  /v. 

•t.  -f  /> 

(-  A,  i. 

f-  A  A 

Q      1      It 

o   /   // 

0     /     // 

IN-.-.  :« 

\:^  7  5!uio 

n:>  3ii  :.s.-2<> 

60  51  0.70 

9.5708516 

:>.!>:u7:>n 

!).55!)3398 

5 

K;I  -21  3.V27 

72  50  33..V, 

ni  7  :«  ;.(>:> 

9.5039252 

9.9400684 

9.5720679 

r- 

K;I  :i:>  1N.-20 

71;  I  16.50 

(17  -^i  is.'ii; 

!).  |-j:!7(ill 

9.9468769 

9.5880998 

9 

1(>7  1!)  S.  l!l 

7!)  IN  (5.79 

70  :5.">  il.'J-.' 

y.:w:{.r)(is  l 

9.9522237 

9.59-25170 

ll 

171  3  r>.7(i 

:i'2   1.07 

73  W  (i.  IN 

9.1911412 

9,9561415 

9.6003850 

13 

171  17  9.75 

s.-i  Hi  M.Oli 

77  3  10.15 

8.9973798 

9.958(5533 

!).(i()(i7.r.li:) 

Dal.-,  1-71 

log  I. 

log  y. 

log  :. 

X. 

y- 

i 

Dec.  3 

9.4282640 

9.7896669 

9.4173623 

+  0.26S0798 

+  0.6161-2-23 

+  0.'2613i;si) 

5 

9.36  16935 

9.7978367 

9.4998362 

0.2-299818 

0.6-27N-2-23 

0.-2(i!)05-20 

7 

9.-2H  1390-2 

9.8045060 

9,1  107-^89 

0.1911570 

0.6375879 

0.2758855 

9 

9.1810(537 

!).K097190 

9.4500123 

0.1517273 

0.645-2366 

0.2818463 

11 

9.0  185083 

9.8185086 

9.4577521 

0.1118171 

0.6508!)  15 

0.-2N(i!)l  1-2 

IS 

8.851(5-251 

9.8188986 

!),!<)  100  18 

+0.07155-25 

+0.6511833 

+  0.-29107-2!> 

TABLE   XI.ll. 


I):iti:,l874. 

Factors  (or 

Pert,  of  the 

Lat. 

A  *• 

Ay- 

AZ. 

A  i- 

A  y. 

A  z- 

llr,-.         3 

13 

+0.001 
0.000 

-0.147 
-0.141 

+  0.323 
+  0.3-21 

+  7 
+  14 

0 
0 

j 
-2 

+2 
+  4 

Dal.-,  1-71 

X. 

jr. 

s. 

Date,  1874. 

a;. 

y- 

z. 

l>rr.        3 

5 

7 

+0.2680798 
0.2299818 
+0.1911570 

+  0.6161222 
().(i-27s-2-2-2 
+0.6375377 

+0.2613682 
0.2690523 

+0.2758858 

Dec.      9 
11 
13 

+0.1517273 
0.1118171 
+0.07155-25 

+  0.6452364 
0.6508913 
+0.6544831 

+  0.2818167 
0.28(59146 
+  0.2910733 

"2.  Required  the  heliocentric  longitude  and  latitude  and  the  logarithm  of  the  radius  vector  of  Venus  for  1769, 
June  3'1   101'   10™  Paris  mean  time. 

This  is  equivalent  to  June  3d  4b  52m  268.98  Washington  mean  time  =  154d.20309  from  the  beginning  of 

the  year. 

Preparation  of  the  Arguments. 


m 

I. 

11. 

111. 

IV. 

V. 

VI. 

VII 

VIII. 

IX 

Table  VI.,  1769     . 

1  ):i\  .if  Yoiir 
Table  V.,  Periods  . 

Arguments  for  date 

-132 
1 

148.1850 
154.2031 
-224.7008 

86.9 
0.4 

6195 
154 

a 
465 
151 

276,8 

154.2 

430.08 

154.20 
—  583.92 

162.6 
151.2 
-243.2 

d 

158.4 
154.2 
-220.6 

95.51 
151.  -20 
—236.99 

-131 

77.6873 

87.3 

6349 

619 

431.0 

0.31 

73.6 

92.0 

12.72 

X. 

XI. 

XII. 

XIII. 

XIV. 

log  sin  i. 

3600  -a. 

XV. 

XVI. 

Tables  VI.,  XXXIX, 
1769     .          ... 

54.98 
33.26 
-60.00 

210.46 
147.64 

-240.00 

57.1 
19.6 
-60.0 

34.91 
3.11 

10.0 
0.8 

8.7721047 
5 

285  23  59^5 
-13.7 

1646.5 

154.2 

,1 
2.3 
154.2 

Tables  V.,  VII.      .     . 

Args.,  &c.,  for  date    . 

28.24 

118.10 

16.7 

38.02 

10.N 

8.7721052 

285  23  45.8 

1800.7 

156.5 

19 


INTRODUCTION. 


Mean  Longitude. 


L. 


Table  VI.,  1769 
Table  VII.,  June  3 
Table  IX.  41' 

tt          tt       52m 

"       "     26S.98 

VIII.,  1769,  (-0" 


Table 

Mean  Longitude, 


4  57     7.69 
246  44     2.33 
16     1.301 
3  28.282 
1.801 
.015  X  0.4)  =  -0.006 


252     0  41.40 


Longitude. 


Logarithm  Radius  Vector. 


Mean  Longitude 

252    6  4L40 

Log.  Elliptic  r,  Table  XXVI., 

9.8610042 

Equation  of  tbe  Centre 

1  25  39.70 

Table  XXVII.,  -  7.66  X  (-  131) 

+  1003 

Table  XI.,  -  10.363  X  (-  131) 

-f  13.57 

Table  XXV1IL,  +  1.2  X  (-.1.31)2 

+       2 

Table  XII.,  +  1.66  X  (-  1.31)2 

+  0.03 

Table  XXIX., 

1716 

Table  XIII., 

4.66 

Table  XXX., 

6 

Table  XIV., 

0.32 

Table  XXXI., 

600 

Table  XV., 

1.12 

Table  XVI., 

4.45 

Arg.  I.             72             80 

Table  XVII., 

16.68 

Table  XVIII., 

2.05 

Table  XXXII.,      48             49 

Table  XIX., 

1.21 

Table  XXXIII.,     39             36 

Table  XX., 

2.93 

Table  XXXIV.,      40              51 

Table  XXXV.,       82             77 

Arg.  L,             72             80 

Table  XXXVI.,      14              10 

Table  XXI.,            82             80 

Sums,             223            223 

Table  XXII.,         145            150 

Interpolated, 

223 

Table  XXIII.,         10                8 

Table  XXIV.,        310           308 

Log.  r, 

9.8610377 

Table  XXV.,            15              17 

Sums               562           563 

Latitude. 

Interpolated, 

5.63 

O            /             // 

Orbit  Longitude, 

253  27  13.75 

Orbit  Longitude, 

253  27  13.75 

360°  -  Q, 

285  23  45.8 

Red.  to  Ecliptic,  Table  XLVL, 

+7.26 

Lunar  Nutation,  Table  XL., 

+  17.29 

Arg.  of  Latitude, 

178  50  59.5 

Solar  Nutation,  Table  XLL, 

-  0.68 

Log  sin  Arg.  of  Latitude, 

8.3025984 

Heliocentric  Longitude, 

253  27  37.62 

Log  sin  i 

8.7721052 

Log  sin  Latitude 

7.0747036 

Elliptic  Latitude 

o          /          // 

+  04    4.98 

Arg.  I.                     72             SO 

Table  XXXVII.,            65             57 

Table  XXXVIII.,          17              15 

Sums                        82              72 

Interpolated 

0.75 

Constant 

-  0.83 

Latitude 

+  04     4.90 

20 

INTRODUCTION. 


Kncke's  reduction  of  tho  observations  of  the  Transit  of  Venus  in  17(!i)  gives  253*  27'  13".  17  and  +0"  4'  4".5fi 
as  the  orbit  longitude  and  latitude.*  I'.ut  according  to  the  Tnhlrx  tin  So/ril  of  Hansen  and  Olufsen,  the  longitude 
and  latitude  of  tin-  Sun,  adopted  b)  Kncke,  must  be  eorreeteil,  respectively,  by  +  0".G4  and  +  0".01.  Thus  we 
ina\  adopt  2.~i3°  27'  13".81  and  +0°  4'  4".52  as  the  values  given  by  observation,  ;uid  the  residuals,  ( )hs.  —  Cal., 
are  respectively  +  0".06  and  —  0".38. 

If  Enekc's  reduction  of  the  Transit  of  1761  is  compared  with  the  Tables,  in  the  same  way,  the  residuals  will 
DC  found  to  be  —  0".33  and  +  0".40. 

3.  Required  the  heliocentric  position  of  Venus  for  1639,  Dec.  I'1  3h  llm  55"  Paris  mean  time. 
This  time  is  equivalent  to  Dec.  3tl  22h  '27'"  21S.9H  Washington  mean  time  =  337'1.93567  from  the  beginning 
of  the  year. 

Preparation  of  the  Arguments. 


lit 

1. 

u. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

IX. 

Table  VI..  1KJ9        . 
Table  XI,  IV,  1600. 
Terms  X  (f  —  50), 
Dav  of  Year, 
Periods,    .... 

-    18 

-326 
+     2 

96.2956 

204.4585 
+0.0005 
337.9357 
-449.4016 

i.-)6:9 

38.9 
0.9 

7786 
10863 

338 

-11987 

2358 
932 

338 

-2959 

1108d9 
1153.7 

337.9 
-1454.9 

303.49 
526.09 

337.94 
-583.92 

196.3 
144.6 

337.9 
-486.3 

138.7 
180.0 

337.9 
-440.1 

66.39 
182.50 

337.94 
-473.98 

Arguments  for  date, 

-342 

191.2887 

196.7 

7000 

669 

1145.6 

583.60 

192.5 

216.5 

112.85 

X 

XI. 

XII. 

XIII. 

XIV. 

log  sin  i. 

*»°-Q. 

XV. 

XVI. 

Tab^s     VI.,      X.XXIX. 

1839     ' 

6.46 

1.97 

14.4 

29.66 

237 

87721999 

a        1        II 

284  46    46 

d 

194 

a 
1  3 

Table  XUV.,  1600     . 

Terms   X  (>'  -  50),    . 

1  Li  \  of  Year,  or  Periods 
Periods     

17.69 
6.52 

107.80 
55.29 

22.2 

39.3 
—  600 

5.56 
6.22 

6.9 
1.5 

-0.0002732 
-24 
+  12 

+  1  48  17.0 
0.6 
30.1 

1732.9 
337.9 

+0.4 
337.9 

Arguments  for  date,  . 

30.67 

165.06 

15.9 

41.44 

32.1 

8.7719255 

286  33  50.9 

2090.2 

339.6 

Mean  Longitude. 

L. 

O  /  // 

Table  VI.,  1839  285  59  48.72 

Table  XLIV.,  1600,  324  46  55.79 

Term  X  (''  -  50),  +  0.458 

Table  VII.,  Dec.  3,  179  55  51.07 

Table  IX.,  221',  1  28    7.157 

"       "     271",  1  48.146 

"       "     219.98,  1.466 

Table  XLV.,  1839.9  with  opp.  sign,  —0.176 

"       "         1942.3  =  1639.9  +  302.4,  —0.279 

Mean  Longitude,  72  12  32.35 


*  Der  Venns-clurolignng  von  17GO,  p.  1(17. 
21 


INTRODUCTION. 


Longituilr. 

Mi -:ni  Longitude, 

Kipmtion  of  the  Outre, 

Table  XI.,  +  lO.JJO!)  X  (-  3 12), 

Table  XII.,  -  1.61  X  (3.12)', 

Table  XIII., 

Table  XIV., 

Table  XV.. 

Table  XVI., 

Table  XVII., 

Table  XVIII., 

Table  XIX., 

Table  XX., 


Arg.  I. 

184 

102 

Table  XXI., 

107 

109 

Table  XXII., 

140 

142 

Table  XXIII, 

25 

25 

Table  XXIV., 

428 

436 

Table  XXV., 

35 

34 

Sums 

735 

746 

Interpolated 

Orbit  Longitude, 
Red.  to  Ecliptic,  Table  XLVI., 
Lunar  Nutation,  Table  XL., 
Solar  Nutation,  XLI., 

Heliocentric  Longitude, 


72   12  32.35 

9     1.83 

-35.26 

-0.19 

1.60 

0.59 

1.27 

2.87 

16.67 

1.30 

0.01 

2.69 


7.45 


72  21  33.18 

+6.79 

+ 16.34 

-  0.73 

72  21  55.58 


Logarithm  Radius  Vector. 

Log.  Elliptic  r,  Tnbl.>  XXVI, 
Table  XXVIL,  +  7.86  X  (-  342), 
Table  XXVIII., 
Table  XXIX., 
Table  XXX., 
Table  XXXI., 


Arg.  I. 

184 

192 

Table  XXXII., 

24 

28 

Table  XXXIII., 

210 

212 

Table  XXXIV., 

108 

96 

Table  XXXV., 

35 

52 

Table  XXXVI., 

26 

20 

Sums  403 

Interpolated 

Log.  r, 


408 


Latitude. 


Orbit  Longitude, 
360°-  Q, 

Arg.  of  Latitude, 
Log  sin  Arg.  of  Lat. 
Log  sin  i, 

Log  sin  Latitude, 

Elliptic  Latitude, 

Arg.  I.  184 

Table  XXXVII.,          54 


Table  XXXVIII., 

Sums 

Interpolated, 
Constant 

Latitude, 


9 
63 


192 

61 
12 

73 


9.8575552 
-2697 
15 

1716 

321 

9 


408 


9.8575527 


72  21  33.18 
286  33  50.9 

358  55  24.1 

n  8.2739219 

8.7719255 

n  7.0 158  17  I 

o          /          // 

-0     3  49.23 


0.72 
-0.83 


-0    3  49.34 


If  Enckc's  reduction  of  Horrox's  observations  of  (be  Transit  at  this  time  be  corrected  to  conform  with  the 
position  of  the  Sun  as  derived  from  Hanson  and  Olufscn's  Tables,  the  residuals  of  the  orbit  longitude  and  helio- 
centric  latitude  arc  found  to  be  respectively  +  1 1".4  and  —  18". 9. 


22 


INTRODUCTION. 
CORRECTION  OF  THE  ELEMENTS  OF  THE  ORBIT  OF  VENUS. 

Tin'  Elements  adopted  tor  comparison  with  oh.-ervation,  arc.  in   the   main,  those  on  which  LKVKIUUKR  \\;\-~ 

\\i-i  Tables. 
They  arc  — 

Epoch,   IViO,  Jan.  1.0,  Paris  Mean  Time. 


-'  =  129  27   1  1.5 

Q'  =  75  19  52.3 

/'  =  3  23  31.83 

c'  =  0.00(581331 

«'  =  21  06(51  1 


The  value  of  «'  has  iii-cn  changed  in  order  to  make  the  adopted  tropical  motion  coincide  with  LKVKKRIKK'S 
value.  The  values  ot  the  disturbing  masses,  and,  in  fuel,  of  all  the  constants  needed  in  the  theory,  are,  with  two 
exceptions,  those  i;iven  ill  the  Introduction.  But  the  annual  tropical  motion  of  the  node  at  the  epoch  1850 
employed  is  32".2!)31  as  it  results  from  the  adopted  values  of  the  planetry  masses  :  and  the  true  longitude  of  tho 
Sim  is  derived  from  the  apparent  longitude  of  I  IAX.SKX'S  and  OLUFSEN'S  Tables  du  Soleil  by  subtracting  the  effect 
of  aherration  Corresponding  to  the  constant  20".2.">5. 

All  the  elements,  except  the  mean  motion,  are  '  determined,  with  nearly  all  the  precision  possible  by  tho 
modern  observations;  that  is  to  say,  those  comprehended  in  the  interval  from  1686  up  to  toe  present  time.  The 
addition  of  the  observations  made  previously  to  183(5  to  the  discussion,  would  scarcely  increase  this  precision. 
For  the  mean  motion  we  must  employ  ancient  observations  ;  anil  for  this  purpose  it  seems  better  to  depend  on  the 
data  furnished  by  the  Transits  of  17(il  and  17(5!),  than  on  the  somewhat  uncertain  observations  of  Bradley. 

Encke's  reduction  of  these  Transits,  corrected  to  conform  with  the  positions  of  the  Sun  derived  from  the 
Tiililm  dn  Soli'H,  will  be  adopted.  All  the  longitudes  mentioned  hero  are  referred  to  the  mean  equinox  of  date. 

For  the  Transit  of  17(51  Encke  gives 

Paris  Moan  Time  =  1761,  June  5d  17h  30'". 

Q  f  II 

True  Longitude  of  the  Sun         =  75  35  49.6, 

Latitude  of  the  Sun  +  0.6, 

Orbit  Longitude  of  Venus            =  2553534.45, 

Heliocentric  Latitude  of  Venus  =  —  3  45.91, 

Hut  the  Tnbli-x  ilit  So/i'  it  give  75°  35'  52".05  and  -f  0".53  as  the  longitude  and  latitude  of  the  Sun.     Consequently 
the  adopted  position  of  Venus  is 

o       /      // 
Orbit  Longitude  =    255  35  36.90, 

Heliocentric  Latitude     =         —   3  45.84. 
For  the  Transit  of  1769,  Enckc  gives 

Paris  Mean  Time  =  17(59,  June  3'1  101'  10'". 

a        I        II 

True  Longitude  of  the  Sun          =  73  27   13.8, 

Latitude  of  the  Sun                        =  0.0, 

Orbit  Longitude  of  Venus           =  2532713.17, 

Heliocentric  Latitude  of  Venus  =  +4     4.56. 

The   Tn/>li'n  /In  N«/a/  give  73°  27'  14".25  and   -f-0".04  as  the  longitude  and  latitude  of  the  Sun.     Consequently 
the  adopted  position  of  Venus  is 

O  I  II 

Orbit  Longitude  of  Venus  =    253  27  13.62, 

Heliocentric  Latitude  of  Venus  =         +4     4.52. 

23 


INTRODUCTION. 

The  meridian  observations  have  been  corrected  to  conform  with  the  constant  8".848  of  solar  parallax,  anil  to 
the  following  expression  for  the  semi-diameter  : 

8^516        Q//  -; 

A 

In  other  respects  Leverricr's  reduction  has  been  adopted.  With  regard  to  the  Greenwich  and  Paris  observations 
which  have  accumulated  since  Levcrricr  made  his  investigation,  that  is,  from  1858  forward,  as,  on  comparing  the 
places,  given  in  the  several  annual  volumes,  for  the  fundamental  time-stars,  with  Dr.  GOULD'S  Standard  Places, 
SfC.,  no  sensible  average  difference  in  the  right  ascensions  could  be  discovered,  no  correction  for  difference  of 
equinoxes  has  been  applied  to  them.  To  the  Washington  observations  in  declination  in  the  years  LS66,  1867, 
has  been  applied  the  correction  +0".7f>.  (Sec  Washington  Observations  for  1867,  Appendix  III.,  pp.  20,  21.) 

In  forming  the  following  normals,  Paris  observations  have  been  combined  with  Greenwich;  but  Washington 
observations  have  been  kept  separate.  The  normals,  formed  from  them,  are  those  given  for  Washington  Mean  Noon. 
The  Paris  Observations  used  are  not  in  great  number,  and  belong  to  the  years  1838  and  1856 — 1866.  The  com- 
parisons arc  Obs.  —  Cal. 

Normals  in  the  inferior  part  of  the   Orbit. 


No. 

Greenwich  M.  T. 

App.  K.  A. 

App.  Dec. 

No.  Obs. 

A« 

A, 

d 

h   in    H 

all' 

8 

n 

1 

1836,  June   9.0 

8  16  6.380 

--21  53  40.12 

4 

+  0.082 

+  0.62 

2 

July    2.0 

8  52  43.140 

--  16  16  11.35 

5 

—  0.057 

+  0.63 

3 

July   K5.0 

8  43  59.799 

--•14  17  35.12 

4 

—  0.054 

—  0.32 

4 

Aug.   7.0 

7  47  48.091 

--13  41  44.35 

3 

+  0.228 

—  0.60 

5 

Aug.  30.0 

7  56  5.580 

--  15  11  1.98 

4 

+  0.083 

—  1.71 

6 

1838,  Jan.   12.0 

22  36  4.483 

-  8  23  42.65 

' 

+  0.079 

+  0.48 

7 

Feb.    2.0 

23  19  4.936 

—  0  5  1.83 

5 

-0.163 

+  5.07 

8 

Feb.  22.0 

23  11  48.498 

+  3  26  16.93 

3 

+  0.050 

+  2.00 

9 

March  12.0 

22  33  39.400 

—  0  1  38.66 

3 

+  0.178 

+  1.75 

10 

March  24.0 

22  23  12.226 

-  3  12  55.39 

10 

+  0.111 

—  1.18 

11 

April   7.0 

22  37  31.008 

-  4  49  5.56 

13 

+  0.096 

—  1.02 

12 

1839,  Sept.  21.0 

12  58  21.552 

—  14  51  58.87 

4 

—  0.147 

—  0.66 

13 

Oct.   12.0 

12  19  41.626 

—  9  44  43.41 

9 

+  0.047 

+  O.S2 

14 

1841,  May   1.0 

3  50  40.864 

+  25  34  44.55 

6 

+  0.009 

+  0.39 

15 

May  27.0 

2  59  23.728 

+  17  13  40.10 

5 

f  0.254 

+  1.95 

16 

June  12.0 

2  59  45.783 

+  14  23  34.07 

4 

-0.021 

—  0.92 

17 

1842,  Dec.   15.0 

17  56  8.706 

—  22  32  23.92 

5 

-0.140 

+  2.34 

18 

1843,  Jan.   10.0 

17  15  35.705 

—  17  35  57.26 

2 

-  0.042 

+  0.29 

19 

1844,  May  31.0 

7  46  25.585 

+  23  55  35.09 

6 

—  0.047 

+  1.23 

20 

July   30.0 

7  49  49.182 

+  13  59  37.34 

6 

—  0.046 

—  0.68 

21 

1846,  Jan.   16.0 

22  44  36.217 

—  6  45  4.41 

3 

—  0.074 

+  0.13 

22 

Feb.    8.0 

23  14  37.585 

+  1  8  50.95 

4 

—  0.092 

+  0.20 

23 

March  18.0 

22  15  8.390 

—  3  5  52.55 

2 

+  0.210 

—  3.17 

24 

1847,  Aug.  15.0 

12  16  12.840 

—  4  47  4.42 

4 

+  0.052 

+  0.69 

25 

Sept.  23.0 

12  43  32.402 

—  13  41  51.42 

4 

—  0.203 

+  0.64 

26 

Nov.  15.0 

12  36  33.246 

—  3  37  36.16 

5 

+  0.206 

-  0.82 

27 

1849,  May   2.0 

3  36  3.678 

+  24  41  22.91 

5 

+  0.187 

+  0.09 

28 

June   8.0 

2  49  10.035 

+  14  4  37.76 

10 

-  0.087 

+  3.60 

29 

1850,  Nov.  23.0 

18  8  47.037 

—  26  55  13.20 

3 

-0.159 

—  2.65 

30 

Dec.  17.0 

17  33  52.085 

—  21  38  46.95 

2 

—  0.033 

—  0,17 

31 

1851,  Jan.   20.0 

17  20  48.740 

—  17  41  28.31 

4 

+  0.296 

—  0.76 

32 

1852,  July   10.0 

8  24  23.066 

+  15  40  33.60 

9 

+  0.040 

+  0.44 

33 

Aug.  16.0 

7  25  42.850 

+  15  24  38.50 

4 

+  0.182 

—  0.78 

34 

Sept.   5.0 

8  4  29.218 

+  15  58  35.33 

4 

+  0.126 

—  1.14 

35 

1854,  Jan.   20.0 

22  50  6.361 

—  5  16  4.06 

6 

+  0.061 

-0.04 

36 

Feb.   3.0 

23  6  4.528 

—  0  34  39.68 

3 

+  0.012 

+  1.67 

37 

Feb.  20.0 

22  49  33.074 

+  1  19  46.87 

5 

+  0.221 

+  0,45 

38 

1855,  Aug.  18.0 

12  20  36.824 

-  5  57  52.34 

7 

+  0.007 

+  0.32 

39 

Sept.  20.0 

12  35  48.073 

-  12  52  25.49 

5 

--  0.120 

+  2.32 

40 

Oct.   12.0 

11  55  6.943 

—  6  28  37.38 

4 

-  -  0.076 

—  1.62 

41 

Nov.  16.0 

12  36  57.050 

-  3  23  38.44 

5 

--  0.148 

—  0.90 

42 

1857,  Feb.   16.0 

0  49  21.025 

+  6  27  10.65     13 

-  -  0.063 

+  0.46 

43 

March  18.0 

2  36  3.575 

+  19  31  12.35      5 

—  0.058 

—  0.37 

44 

April  16.0 

3  35  55.521 

+  25  33  57.52      7 

+  0.027 

—  0.85 

45 

May  21.0 

24250.763     +165935.65      8     +0.118 

+  0.56 

46 

June   13.0 

2  50  20.725     +  13  31  18.27     13     +  0.020 

+  0.81 

24 


INTRODUCTION. 


No. 

GrciMiwii-li  M.  T. 

App.  K.  A. 

App.  1  > 

.V,   01,, 

An 

A-i 

.1 

ll          III             fl 

off/ 

| 

// 

17 

1*57.  June      26.0 

3  20    19.536 

+  11  46    16.18 

12 

+  0.08  1 

+  1.07 

18 

1858,  AMU.     17.0 

12  21     4.321 

-    2    10  32.51 

!) 

-0.139 

+  1.03 

I!) 

Sept.     18.0 

11  31   :>7.:>11 

-  17  21    17.16 

4 

—  0.05*. 

—  1.56 

50 

(  tet      10.0 

16     2      1.666 

-24    12    17.26 

10 

—  O.ON6 

-  0.62 

51 

Nov.      7.0 

17  37    19.017 

—  28      1   51.96 

11 

+  0.050 

—  3.2  1 

V,v.    29.0 

17  55    !).<;:>!          —  25  :>i  3i.n 

3 

+  0.311 

-4.70 

53 

!)«-.     21.0 

17     7   52.155 

—  20     4   43.16 

4 

+  0.203 

—  2.23 

54 

IS.')!),   .Ian.        10.0 

16  5S  27.618 

—  17   21   53.14 

7 

+  0.051 

+  3.60 

55 

.l:ill.        29.0 

17    10  25.353                   is  26     821 

8 

+  0.138 

+  0.17 

56 

I860.   M;IV        ;{.() 

5  53    lts.561            +26  36  37.27 

4 

+  0.03  1 

+  1.13 

57 

.M:iv     23.0 

7  16     2.x  13 

+  25  23  36.95 

5 

+  0.0)2 

+  1.53 

58 

June      lit!) 

s  23  55.S23 

-  19  58  30.  1  1 

5 

f  0.103 

+  2.  13 

59 

July       10.0 

8  11    15.899 

-  16     8  22.57 

6 

+  0.103 

+  2.50 

60 

An;,'.    31.0 

7  4N   10.699 

-  16  21   11.53 

7 

+  0.203 

+  0.18 

61 

Sept.    22.0 

!)      1   57.720 

-  14   11  21.01 

11 

+  0.174 

-0.67 

89 

1861,  Doc.      10.0 

20  31   32.S10 

—  21     9  42.31 

4 

—  0.020 

-  1.11 

68 

Dec.     26  0 

21   37   51.N53 

-15  29   11.52 

7 

+  0.036 

-  1.41 

(it 

1862,  Jan.      16.0 

22  38  21.3S1 

-    6  59     2.66 

9 

+  0.063 

—  0.43 

66 

Feb.      12.0 

22  50  59.987 

+    0  17  57.58 

2 

+  0.201 

—  2.41 

66 

March    11.0 

21   58  59.897 

-    3  59  31.67 

5 

+  0.211 

+  3.72 

67 

April    23.0 

23   14     6.685 

4  20  27.06 

9 

f  0.061 

+  0.09 

68 

.May      13.0 

0  26     3.  17!) 

+    1   19  59.00 

4 

-  0.069 

+  2.83 

69 

1863,  July      11.0 

10  21  37.937 

+  10  53  34.89 

7 

-  0.014 

+  0.74 

70 

An"},'.       1.0 

11   35     5.196 

+    1  22     1.05 

6 

-  0.004 

—  2.34 

71 

lug.      12.0 

12      1  25.882 

-    3  26  49.57 

7 

+  0.106 

—  4.25 

n 

Sept.     i.o 

12  35  55.785 

-  10  23  46.78 

6 

-0.108 

+  0.38 

73 

Sept.     !!).() 

12  21   5  1.20C 

-  11   49  46.67 

6 

+  0.117 

+  1.85 

'  1 

Oct     2s.o 

11    50  36.106 

—    1   43  20.76 

2 

+  0.117 

—  3.63 

75 

NOT.    20.0 

12  47   33.27  1 

—    3  53  37.08 

5 

+  0.202 

-2.15 

76 

1865,   Feb.      13.0 

0  38  41.720 

-58     4.61 

4 

—  0.012 

-  1.17 

77 

March  25.0 

2  51     9.362 

-21  44  33.17 

7 

—  0.008 

+  0.69 

78 

April       9.0 

3  23      1.559 

-21    16  29.99 

10 

+  0.057 

+  0.96 

78 

April    25.0 

3  20  45.JJ53 

-21  31   33.5!) 

11 

+  0.102 

—  0.08 

NO 

May        7.0 

2  56  28.201 

+  21     8     3.49 

7 

+  0.201 

+  1.48 

81 

May      21.0 

2  28  59.092 

-  14  58  17.96 

9 

+  0.233            +  1.59 

83 

June     11.0 

2    12    18.317 

-  13    4  19.64 

8 

+  0.208           +  0.26 

83 

June     22.0 

3     7  28.235 

-  14     5  20.47 

7 

+  0.139 

—  0.07 

84 

July      11.0 

4     9  16.618 

-17  22     1.01 

9 

+  0  106 

+  0.31 

85 

1866,  Sept.    25.0 

15     1   14.407 

—  20  15  30.52 

3 

+  0.066 

+  0.55 

86 

Oct.      16.0 

16  24  17.041 

—  26     5  30.30 

7 

+  0.017 

—  1.53 

87 

Oct.     27.0 

17     2  22.875 

—  27  36  58.50 

3 

—  0.002 

+  0.46 

88 

Nov.     15.0 

17  44  28.584 

—  27  42  20.26 

9 

-  -  0.208 

-0.31 

86 

Nov.     30.0 

17  39     2,104 

—  25  25  42.81 

4 

--  0.417 

+  0.05 

90 

Dec.     28.0 

16  44  36.668 

-  18    5  53.53 

2 

-.  0.359            +0.19 

91 

1867,  Feb.       7.0 

18     9  47.537 

—  19    2  58.09 

6 

--  0.174            +1.04 

99 

March  30.0 

21  52  48.772 

—  12  51  21.47 

2 

--0.015            —0.29 

93 

1868,  May       6.0 

6    7  11.8:51 

-26  42  54.56 

6 

—  0.  1  1  1 

+  0.76 

94 

May      19.0 

7    0  21.501 

-25  57     6.61 

3 

+  0.05  1            +  0.95 

95 

May      29.0 

7   31   52.111) 

-21   29  40.91 

4 

+  0.103            +0.71 

96 

June      12.0 

8     8  50.822 

-21    11   50.55 

9 

+  0.05!)            +  0.79 

97 

June     29.0 

8  16  30.999            +  18  13  10.72 

7 

+  0.203 

—  0.09 

98 

July      14.0 

7  47     9.381 

-  16     9  52.23 

6 

+  0.  177 

+  1.23 

99 

July      28.0 

7  14  21.065 

-  15  34    15.57 

4 

+  0.173 

—  1.35 

100 

Aug.     15.0 

7  11  41.426 

-16   13  52.9!) 

1 

+  0.050 

—  0.96 

101 

Aug.    26.0 

7  32  23.633 

-  16  38  18.77 

4 

+  0.104 

+  0.03 

102 

Sept.         4.0 

7  57  43.509 

-  16  35     5.21 

4 

—  0.069 

—  0.37 

103 

Sept.       18.0 

8  46  43.419 

-  15  25  27.66 

6 

+  0.00  1 

—  0.63 

104 

1869,  Doc.        1.0 

19  55     0.713 

—  23  33  19.35 

2 

+  0.033 

+  0.09 

105 

Dec.     23.0 

21  26  28.614 

—  16  37  52.39 

1 

+  0.038 

+  0.94 

106 

1870,  Jan.         3.0 

22     2  46.591 

-12  18    0.76 

1 

+  0.092            +  1.72 

107 

Jan.      27.0 

22  48  13.855 

-    3  24  26.46 

4 

+  0.339            +  2.6  1 

108 

Feb.     21.0 

22    19    12.992 

—    1    14   10.51              3 

+  0.257            +  2.49 

109 

March  19.0 

21  49     6.160 

-    6  42  37.21              2 

+  0.196           +1.21 

110 

April      5.0 

22   18  31.S56 

-    7   18  36.33              2 

+  0.087            +  2.55 

111 

April     12.0 

22  37  59.072 

—    6  36    2.61             3 

+  0.266            +  2.67 

119 

April    22.0 

23   10     0.139                     1    16  21.21               3            +0.060            +2.31 

4  V 


25 


INTRODUCTION. 


No. 

Greenwich  .M.  T. 

.\pp.  R.  A. 

AI>]>.  D'-c.    . 

No.Obs. 

A« 

A<! 

(i 

ll           11)            S 

0            I            It 

s 

// 

113 

1H70,  May     23.0 

1     5  55.5  18 

+    4  54  43.03 

7 

+  0.036 

+  0.63 

111 

June     13.0 

2  33  32.  55N 

4-  12  34  56.06 

4 

+  0.148 

-0.12 

115 

July      13.0 

4  53     4.820 

-j-20  50  51.48 

5 

+  0.047 

+  1.00 

116 

Aug.      S.O 

7     5  26.170 

4-22     6  39.93 

3 

-  0.032 

!-  i.oo 

117 

Aug.    '25.0 

8  32   16.460 

|-  19   12     2.24 

5 

—  0.107 

+  0.3  I 

18 

Sept.     15.0 

10  14  53.930 

(-  12     4     3.63 

2 

—  0.060 

+  0.89 

li) 

Sept.     '26.0 

11     6  24.896 

-    7   13  14.54 

5 

—  0.026 

+  0.78 

20 

Oct.      1-2.0 

12   19  50.532 

—    0  31  51.43 

5 

—  0.170 

+  1.03 

•21 

Nov.       i.O 

13  52  35.280 

—  10  14  46.16 

4 

—  0.157 

-  0.24 

23 

Nov.     18.0 

15   15  37.167 

—  17  20  12.09 

3 

—  0.012 

+  1.06 

123 

Dec.     -21.0 

18  28     7.770 

—  23  56   17.07 

1 

-  0  033 

-  1.33 

124 

l:i~l,  Jan.        4.0 

19  28  19.110 

-22  55     7.73 

1 

—  0.029 

+  1.12 

No. 

Wellington  -M.  T. 

A|»i>.  1!.  A. 

App.  Dei'. 

No.Obs. 

An 

A'i 

.1 

li        in         s 

0            /            // 

B 

// 

1  25 

1863,  Aug.     19.0 

12  19  46.295 

—    6   19  30.41 

13 

+  0.078 

+  1.33 

126 

Sept.     1-2.0 

12  34     6.510 

-  12     5  24.23 

9 

4-0.071 

+  1.08 

127 

Oct.      19.0 

11  42  32.127 

-    2  57  57.34 

10 

-|-  0.236 

-0.94 

128 

Nov.     15.0 

12  32  43.563 

—    2  56     9.17 

11 

4-0.071 

+  0.35 

1-.") 

1865,  Feb.       7.0 

0   16  19.073 

+    2  10  43.90 

6 

4-  0.034 

+  0.11 

130 

Feb.     -23.0 

1   16  59.279 

-|-  10     9   15.R1 

4 

-  0.039 

--0.44 

131 

March  11.0 

2  13     1.700 

-j-  17     6  32.28 

o 

+  0.037 

-  -  1.02 

132 

March  28.0 

3     2     8.034 

+  22  35  31.27 

o 

—  0.113 

--  1.20 

133 

April    18.0 

3  26  40.672 

4-25  11    16.40 

6 

+  0.010 

--  1.81 

J.-J1 

May       2.0 

3     7  27.361 

-j-22  47  40.20 

4 

+  0.240 

4-0.61 

135 

May       18.0 

2  34  22.761 

+  16  46  48.36 

7 

+  0.091 

+  1.46 

136 

.limr       4.0 

2  32  28.520 

4-13     9     9.64 

8 

+  0.095 

j-0.42 

137 

June     26.0 

3  19  28.164 

4-  14  43  23.83 

9 

+  0.079 

0.00 

138 

July      '20.0 

4  45  13.373 

4-  18  57  33.95 

8 

+  0.080 

+  1.11 

139 

1866,  Sept.     1-2.0 

14     9     6.234 

-  15     7  32.81 

5 

—  0.062 

-  0.62 

110 

Oct.       6.0 

15  46  27.321 

-23  49  35.82 

4 

-  0.031 

-  0.75 

111 

Oct.      19.0 

16  36     2.1)52 

-26  39     2.71 

8 

+  0.061 

-2.11 

142 

Nov.       9.0 

17  36     3.668 

-28     1   18.33 

7 

+  0.134 

-  1.56 

143 

Nov.    28.0 

17  42     2.599 

-25  52     0.26 

6 

+  0.385 

-  1.88 

111 

Dec.     19.0 

16  55  50.052 

-20    0  53.68 

2 

+  0.570 

+  2.20 

145 

1867,  Jan.      22.0 

17  17  25.170 

—  17  59  43.41 

10 

+  0.222 

—  0.14 

Normals  in  the  superior  part  of  the  Orbit. 


No. 

Greenwich  M.  T. 

App.  a.  A. 

App.  Dec. 

No.Obs. 

A« 

At! 

,1 

li       m        s 

0            /            // 

g 

// 

146 

1858,  Jan.      23.0 

19  46  16.637 

—  21  53  48.46 

3 

+  0.022 

—  2.26 

117 

April    23.0 

2  56  59.252 

+  16  35  27.79 

5 

—  0.005 

-0.10 

us 

June     14.0 

7  27  55.977 

+  23  33  18.26 

13 

+  0.078 

-0.13 

119 

July      19.0 

10  17  52.788 

+  12  10  47.22 

5 

—  0.035 

+  0.11 

150 

1859,  Feb.     23.0 

19  14  56.589 

-  19  15  37.66 

7 

+  0.022 

-0.82 

151 

March  18.0 

20  57     4.220 

-  16  1  1   30.29 

6 

+  0.188 

+  2.39 

152 

June     17.0 

3  46  35.988 

+  18  29     1.65 

4 

+  0.033 

-  0.40 

158 

July      19.0 

6  31  41.515 

+  23     6  57.50 

11 

-  0.021 

-  0.31 

164 

Aug.    23.0 

9  32     0.652 

4-  15  49  11.42 

8 

-0.016 

-0.44 

155 

Nov.     13.0 

16     1  34.918 

-20  45  38.42 

5 

+  0.0  14 

-  1.75 

158 

Dec.     17.0 

19     5  56.987 

—  23  55  27.75 

4 

+  0.043 

-  3.39 

157 

1860,  Jan.      17.0 

21  46   14.280 

—  15  10  47.89 

5 

+  0.016 

—  2.66 

158 

Feb.     29.0 

1     0  24.170 

+    6  15  55.78 

3 

-  0  062 

—  0.77 

159 

April    19.0 

4  48  31.013 

-j-25  10  19.92 

4 

-0.014 

-  0.04 

160 

Oct.      24.0 

11    13  17.826 

+    5  r>l  46.41 

5 

+  0.086 

-  0.82 

161 

Dec.     10.0 

14  42  35.914 

-  13  40  52.46 

5 

-  0.060 

—  0.81 

162 

1867,  May      14.0 

1   11     9.973 

+    5  34  41.60 

6 

+  0.113 

+  0.44 

163 

June     17.0 

3  49     8.762 

+  18  38  58.87 

5 

+  0.050 

+  1.11 

16  i 

Aug.     18.0 

9  10     1.066 

+  17  23  4  1.04 

6 

—  0.059 

+  0.60 

165 

Oct.      15.0 

13   11     6.075 

-    9  28  37.18              4 

+  0.009 

—  1.01 

26 


I  INTRODUCTION. 

jYii;'»w/.v    in    I  In-   sii/irrinr  /iiir/   »/'  //»•    Orlil. 


No. 

Gri'cnwirli  M.  T. 

A|i|>.  ft.  A. 

A  ji|i.  n  • 

No.  Ob*. 

Aa 

A.! 

166 

|si;-.  Nov.     19.0 

h       in        a 
16  36     3.11s 

0             /            // 

—  22  2.">  31.:.1 

5 

—  0*001 

-  a:>  i 

167 

1868,  Oct.       16.0 

10    10    13.171 

+    8  3s  :J!I.S2 

9 

+  0.100 

+  0.01 

168 

Dec.     17.0 

15    IS    Hi.5l.Vi 

-  16  23  36.5)5 

6 

+  0.083 

f  0.83 

169 

Is<;<),  .Ian.        12.0 

17  32  57.506 

—  22  22  25.57 

5 

+  o.ino 

1.18 

170 

\:K:|     20.0 

1   36     7.1!).") 

+    8    13  5!).!)5 

6 

-  0.070 

+  0.55 

171 

.lime       17.0 

(i  29  55.7s  1 

+  2!     7   55.16 

5 

-  0.020 

+  0.32 

172 

Jnlv       Ki.O 

9      1     6.0!)0 

+  18  33     2,s7 

1 

-  0.208 

+  0.78 

173 

An-.     2(i.O 

12  10    o.t;si 

-    0     7  31.79 

5 

-0.010 

f  0.29 

174 

Sep,.       21.0 

1  1     :•  2C.  --:;:! 

-13     7    17.72 

1 

—  0.183 

+  1.02 

178 

Oct.       13.0 

15    11)    16.3li8 

-21    12    11.S7 

5 

—  0.026 

+  1.13 

In  order  to  have  as  few  unknown  quantities.  in  the  ci|ii;itioiis  of  condition,  ;i^  possible,  the  dillrrciiccs  J  n  and 
Jo  |i,-i\i.  I  ice  n  i-liiiiiircd  into  cos  rr  J  II  and  J  i,  ;  W  di  -noting  th<'  ^cciccnlric  lon^ilndc  of  Venus  ivl'm-rd  in  a  plane 
dmwii  tlirongli  the  e.-utre  of  the  Kartli  parallel  to  the  plane  of  the  orhil  of  Venus,  and  T,  denoting  the  corresponding 
latitude.  The  forniuhr  used  are  given  in  WATSON'S  T/ii-off/irnl  .\xlrnnomii.  pp.  153  —  159. 

In    the    following   eipiations,  \vc  have  put 

l' 


a;  =  J  L'o-  2  sinj  ','  J  Q', 


y  =  100  J  «', 


c'  (  J  -'  - 


2  t   J 


all  expressed  in  seconds  of  arc;  and  .r',  //',;'  and  u'  denote  the  similar  quantities  in  reference  to  the  solar  ele- 

ments.     In  the  computation  of  the  coefficients  of  the  last,  roughly  approximate  formula;  have  heen  used. 

A  mean  of  the  Transits  of  17G1  and  17G9  gives 

+  0.992  j'  -  0.839  y  +  1.61  :  +  1.17  u  +  1.00  x>  -  0.84  y  +  0.83  z'  -  \.82u'  =  +  1".745. 

The  indeterminate  correction  of  the  Sim's   semi-diameter  nearly  disappears  from  this  mean. 

The  following  equations  of  condition  are  numbered  with  the  same  number  ;>s  the  normals,  from  which  they 
are  derived.  The  last  column  contains  tin;  residuals  which  remain  after  the  elements  have  been  corrected  as 
shown  in  the  sequel. 


No. 

1 
2 
3 
4 
5 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 


Equations  of  condition. 

Residuals. 

-  0.40 *+  O.OSy—  0.36:—  1.44«+  1.4&/  —  0.19/  —  0.21  z'—  3.06u'  =  +  L01  +  0.97 

-1.37    +0.18—0.87—2.97+2.41      -0.32  -1.45  -4.69  =—0.95  —1.02 

-2.05    +0.28—0.87—4.16+3.08      -0.41  -2.17  -5.74  =    -0.69  —0.71 

-2.07    +0.28—0.02—4.28+3.11      -0.41  -2.65  -5.57  =+3.37  +3.37 

-0.80    +0.11+0.31—2.15+1.80      -0.24  -2.22  —3.16  =+1,11  +1,13 

-0.31    +0.04—0.12+1,11+1.30      -0.16  +1.86  +2.32  =+1.27  +0.68 

-0.98    +0.12  —0.93  +2.31  +  1.98      -0.21  +3.56  +2.59  =—0.23  —1.25 

-2.27    +0.27—2.31+4.06+3.27      -0.39  +5.84  +3.12  =+1.48  —0.38 

_--j.  U    +0.29—3.04+3.85+3.10      -0,10  +6.26  +2.85  =+3.13  +1.22 

-1.70    +0.20—2.53+2.69+2.70      -0.32  +5.18  +2.00  =+1.13  —0.27 

-0.90    +0.11—1.76+1.56+1.91      -0.22  +3.95  +1.01  =+0.96  +0.08 

-2.06    +0.21+3.53—2.38+3.08      -0.32  -6.12  -0.14  =—1.66  —2.07 

-2.51    +0.26+4.64—2.02+3.51      -0.36  -7.01  +0.39  =+0.29  —0.34 

-2.00    +0.17—4.12—0.54+3.00      -0.26  +4.57  —3.99  =+0.22  —0.91 

-2.09    +0.18—4.05—1.48+3.10      -0.27  +4.28  -4.47  =+4.08  +3.09 

-1.12    +0.10—2.39—1.18+2.12      -0.14  +2.72  -3.49  =—0.59  —1.11 

-2.69    +0.19+3.71+3.87+3.69      -0.26  -1.82  +7.26  =—2.09  —120 

—  1.58    +0.11  +  1.80  +2.98  +2. 5s      -0.18  -0.65  +5.38  =— O.(i3  -2.10 

0.07  +0.21  -2.76  =    -0.81  (i.id 

0.18  —2.17  +6.18  =—0.57  —1.14 


-  0.27 

-  2.40 


+  0.01  —0.63  —  1.18  +  1.27     - 
+  0.13  —0.41  —  1.N2  +3.10 

27 


INTRODUCTION. 


No. 


Equations  of  condition. 


Residuals. 


21 

-  0.47.T 

+  0.02.y—  0.17-. 

+  1.64«+  1.47^ 

—  0.06y' 

+  2.19;' 

+  2.48w' 

—  —0.98 

—  1.79 

22 

-  1.51 

+  0.06 

—  1.31 

+  3.16 

+  2.54 

—  0.10 

+  1.37 

+  3.00 

-  1.19 

-2.93 

23 

-  1.95 

+  0.07 

-2.61 

+  3.15 

+  2.95 

—  0.11 

+  5.79 

+  2.51 

=  +  1.84 

-  0.20 

21 

-0.40 

+  0.01 

+  1.03 

-  1.15 

+  1.40 

-0.03 

—  2.79 

-1.18 

=  +0.42 

+  0.24 

25 

—  2.29 

+  0.05 

+  8.87 

—  2.60 

+  3.28 

-0.07 

—  6.58 

—  0.29 

=  —2.95 

—  3.92 

26 

—  0.55 

+  0.01 

+  1.78 

—  0.38 

+  1.55 

—  0.03 

—  3.33 

+  1.04 

=  +3.15 

+  2.75 

27 

—  2.22 

+  0.02 

-4.51 

-0.53 

+  3.22 

—  0.02 

+  4.94 

-4.09 

=  +2.47 

+  0.72 

28 

—  1.22 

+  0.01 

—  2.59 

—  1.14 

+  2.22 

—  0.01 

+  3.02 

-3.46 

=  +0.04 

—  0.85 

29 

—  1.55 

-0.01 

+  2.84 

+  1.97 

+  2.55 

+  0.02 

—  2.07 

+  4.94 

=  —2.24 

-3.81 

30 

—  2.73 

—  0.03 

+  3.75 

+  3.93 

+  3.72 

+  0.04 

—  2.06 

+  7.28 

=  —0.41 

—  3.18 

31 

—  0.88 

—  0.01 

+  1.17 

+  2.02 

+  1.88 

+  0.02 

—  1.96 

+  4.10 

=  +4.28 

+  3.11 

32 

—  2.18 

-0.05 

—  1.24 

—  4.31 

+  3.18 

+  0.08 

-L77 

—  6.06 

=  —0.38 

-  1.61 

33 

—  1.26 

-0.03 

+  0.04 

—  2.92 

+  2.26 

+  0.06 

—  2.00 

-4.22 

=  +2.07 

+  1.48 

34 

-0.44 

—  0.01 

+  0.19 

-1.60 

+  1.44 

+  0.04 

—  1.92 

—  2.50 

=  +  1.59 

+  1.39 

35 

—  0.68 

—  0.03 

-0.51 

+  1.96 

+  1.68 

+  0.07 

+  2.58 

+  2.70 

=  +0.46 

-0.68 

36 

-  1.37 

—  0.06 

-  1.02 

+  2.96 

+  2.37 

+  0.10 

+  3.95 

+  3.09 

=  +0.71 

-  1.20 

37 

-2.43 

—  0.10 

-2.15 

+  4.44 

+  3.42 

+  0.14 

+  5.83 

+  3.70 

=  +2.52 

—  0.59 

38 

-0.51 

—  0.03 

+  1.14 

-1.33 

+  1.51 

+  0.09 

-3.10 

-  1.20 

=  —0.19 

—  0.52 

39 

-2.27 

-0.13 

+  3.71 

—  2.77 

+  3.27 

+  0.19 

-6.49 

-0.59 

=  +0.25 

-1.20 

40 

-2.32 

-0.13 

+  4.26 

—  2.04 

+  3.27 

+  0.19 

—  6.59 

-0.07 

=  +  1.31 

-0.27 

41 

—  0.46 

-0.03 

+  1.64 

—  0.39 

+  1.46 

+  0.09 

-3.12 

+  0.99 

=  +2.17 

+  1.73 

42 

+  0.13 

+  0.01 

—  0.89 

+  0.28 

+  0.87 

+  0.06 

+  1.91 

+  0.52 

=  +  1.01 

+  0.85 

43 

—  0.25 

-0.02 

-1.34 

+  0.16 

+  1.21 

+  0.09 

+  2.71 

—  0.68 

=  —0.68 

—  1.18 

44 

—  1.37 

—  0.10 

—  3.10 

+  0.07 

+  2.37 

+  0.17 

+  4.12 

—  2.66 

=  +0.01 

—  1.57 

45 

-2.17 

—  0.16 

-4.30 

-  1.15 

+  3.17 

+  0.23 

+  4.76 

-4.18 

=  +  1.79 

-0.31 

46 

—  0.86 

—  0.06 

—  2.06 

-0.91 

+  1.86 

+  0.14 

+  2.50 

—  3.03 

=  +0.55 

-0.31 

47 

—  0.41 

—  0.03 

—  1.38 

-0.72 

+  1.41 

+  0.11 

+  1.57 

-2.63 

=  +  1.49 

+  1.01 

48 

+  0.28 

+  0.02 

+  0.81 

—  0.23 

+  0.72 

+  0.06 

—  1.45 

-0.59 

=  —2.32 

-2.18 

49 

+  0.13 

+  0.01 

+  0.92 

+  0.17 

+  0.87 

+  0.08 

-  1.91 

+  0,13 

=  —0.21 

-  0.26 

50 

—  0.05 

0.00 

+  1,06 

+  0.48 

+  1.01 

+  0.09 

—  1.96 

+  1.41 

=  —0.98 

—  1.26 

51 

—  0.80 

—  0.07 

+  1.95 

+  1.01 

+  1.79 

+  0.16 

—  2.15 

+  3.30 

=  +0.98 

-0.08 

52 

-2.13 

-0.19 

+  3.57 

+  2.60 

+  3.10 

+  0.28 

—  2.37 

+  5.96 

=  +4.52 

+  1.97 

53 

—  2.58 

-0.23 

+  3.49 

+  3.83 

+  3.54 

+  0.32 

—  2.09 

+  6.93 

=  +3.16 

-0.06 

54 

—  1.28 

-0.12 

+  1.70 

+  2.46 

+  2.26 

+  0.20 

—  0.80 

+  4.79 

=  +0.13 

-  1.67 

55 

—  0.48 

-0.04 

+  0,81 

+  1.49 

+  1.47 

+  0.13 

+  0.19 

+  3.29 

=  +  1.94 

+  1.03 

56 

+  0.09 

+  0.01 

—  0.55 

—  0.78 

+  0,92 

+  0.09 

+  1.02 

-1.78 

=  +0.55 

+  0.58 

57 

-0.17 

—  0.02 

—  0.62 

—  1.07 

+  1.18 

+  0.12 

+  0.55 

—  2.81 

=  +0.44 

+  0.27 

58 

—  1.03 

—  0.11 

—  1.08 

—  2.31 

+  2.05 

+  0.21 

—  0.57 

-4.25 

=  +0.95 

+  0.14 

59 

—  2.27 

—  0.24 

-  1.37 

—  4.41 

+  3.29 

+  0.35 

-1.62 

—  6.32 

=  +  1.02 

—  0.62 

60 

—  0.52 

—  0.05 

+  0.10 

-  1.72 

+  1.52 

+  0.16 

-1.83 

—  2.76 

=  +2.87 

+  2,49 

61 

—  0.06 

—  0.01 

+  0.16 

—  1.09 

+  1.07 

+  0.11 

-  1.89 

—  1.47 

=  +2.61 

+  2.58 

62 

+  0.07 

+  0.01 

—  0.02 

+  1.02 

+  0.92 

+  0.11 

+  0.26 

+  2.12 

=  —0.58 

—  0,88 

63 

-0.12 

—  0.01 

—  0.16 

+  1.21 

+  1.11 

+  0.13 

+  1.00 

+  2.37 

=  +0.07 

-0,48 

61 

—  0.62 

—  0.07 

—  0.36 

+  1.89 

+  1.61 

+  0.19 

+  2.35 

+  2.74 

=  +0.72 

—  0.48 

65 

—  2.12 

-  0.26 

—  1.60 

+  4.07 

+  3.07 

+  0.37 

+  5.13 

+  3.73 

=  +  1.87 

-  1,35 

28 

[NTRODUOTION. 


No. 


Equation*  <>l  cui/di/ion. 


66 

—  2.11. 

,  _  0.26//—  2.45*+  3.60u+  3.07-t'  +  0.37./  +  5.  11-.'  +  3.  15«'  = 

+  4.21 

+  1.01 

67 

o.2:t 

—  0.03 

—  0.97 

+  0.86 

+  1.22 

+  0.15 

+  2.71 

+  0.18 

= 

+  0.87 

+  0.23 

86 

+  0.03 

0.00 

-  O.SO 

+  0.55 

+  0.96 

+  0.12 

+  2.05 

—  0.56 

= 

+  0.23 

-0.06 

69 

+  0.09 

+  0.01 

+  0.47 

-  O.S2 

+  0.92 

+  0.12 

-  1.17 

-  1.65 

= 

-  0.  15 

-0.51 

70 

-0.17 

-  0.02 

+  0.73 

—  1.00 

+  1.18 

+  0.16 

—  2.14 

-  1.1!) 

= 

+  0.89 

+  0.73 

71 

—  0.11 

-  ().().-, 

+  0.98 

—  1.22 

+  l.ll 

+  0.19 

—  2.7!) 

—  1.31 

= 

+  3.22 

+  2.87 

72 

-  1.19 

-0.16 

+  1.98 

—  2.02 

+  2.20 

+  0.30 

-  4.  19 

-  1.05 

= 

-  1.61 

—  2.63 

73 

-  2.2!) 

-O81 

+  3.67 

-  2.8!) 

+  3.29 

+  0.  15 

—  6.57 

—  0.78 

= 

+  0.77 

-1.19 

71 

-  1.13 

—  0.16 

+  2.56 

—  0.97 

+  2.11 

+  0.29 

-  1.55 

+  0.11 

= 

+  3.09 

+  1.95 

75 

-0.31 

—  0.01 

+  1.11 

—  0.36 

+  1.31 

+  0.18 

—  2.7? 

+  1.06 

= 

+  3.6  1 

+  3.21 

74 

+  0.13 

+  0.02 

—  0.88 

+  0.33 

+  0.97 

+  0.15 

+  1.93 

+  0.85 

= 

-  1.08 

-  1.21 

77 

—  0.48 

—  0.07 

-  1.66 

+  0.23 

+  1.61 

+  0.25 

+  3.39 

—  0.81 

= 

+  0.13 

-  0.74 

78 

-  1.09 

-0.17 

—  2.6  1 

+  0.21 

+  2.25 

+  0.3  1 

+  1.25 

—  1.90 

= 

+  1.03 

—  0.58 

79 

—  2.05 

—  0.32 

-  1.2  1 

—  0.17 

+  3.16 

+  0.  IS 

+  5.41 

—  3.27 

= 

+  1.30 

-  1.37 

80 

-2.51 

—  0.39 

-4.99 

—  0.6  1 

+  3.50 

+  0.54 

+  5.80 

—  3.80 

= 

+  3.15 

+  0.05 

81 

-  1.81 

—  0.28 

—  3.75 

—  1.02 

+  2.67 

+  0.11 

+  4.11 

—  3.2  t 

— 

+  3.72 

+  1.53 

82 

-0.78 

-0.1  2 

—  2.03 

-0.71 

+  1.61 

+  0.25 

+  2.66 

—  2.  17 

= 

+  2.94 

+  1.95 

83 

—  0.45 

—  0.07 

-  1.47 

—  0.65 

+  1.27 

+  0.20 

+  1.89 

—  2.22 

= 

+  1.89 

+  1.30 

81 

-0.07 

—  0.01 

—  0.98 

—  0.51 

+  0.94 

+  0.15 

+  0.91 

-2.01 

= 

+  1.51 

+  1.32 

85 

+  0.01 

+  0.01 

+  1.02 

+  0.20 

+  1.08 

+  0.18 

—  2.25 

+  0.55 

= 

+  0.69 

+  0.53 

86 

—  0.2  1 

-  0.0  1 

+  1.28 

+  0.45 

+  1.39 

+  0.23 

—  2.  1!) 

+  1.68 

= 

+  0.95 

+  0.41 

87 

—  ().:>! 

—  0.09 

+  1.62 

+  0.66 

+  1.67 

+  0.28 

—  2.61 

+  2.  17 

= 

—  0.10 

-  1.00 

88 

—  1.36 

—  0.23 

+  2.76 

+  1.48 

+  2.52 

+  0,43 

—  2.92 

+  4.38 

= 

+  2.78 

+  0.78 

89 

—  2.36 

-0.10 

+  3.97 

+  2.75 

+  3.  15 

+  0.58 

—  3.24 

+  6.23 

= 

+  5.62 

+  2.27 

90 

—  1.95 

-0.33 

+  2.75 

+  3.06 

+  2.73 

+  0,46 

-2.12 

+  5.43 

= 

+  4.99 

+  2.07 

91 

—  0.20 

-0.03 

+  0.64 

+  1.14 

+  1.02 

+  0.17 

+  0.16 

+  2.49 

= 

+  2.58 

+  2.00 

92 

+  0.24 

+  0.04 

-0.01 

+  0.86 

+  0.66 

+  0.11 

+  1.23 

+  0.92 

= 

+  0.53 

+  0.47 

93 

+  0.04 

+  0.01 

—  0.58 

—  0.82 

+  0.97 

+  0.18 

+  0.98 

—  1.93 

= 

-1.45 

-1.45 

94 

-0.11 

—  0.02 

—  0.64 

—  1.01 

+  1.15 

+  0.21 

+  0.65 

—  2.46 

= 

+  0.68 

+  0.49 

95 

—  0.35 

—  0.06 

—  0.76 

—  1.27 

+  1.36 

+  0.25 

+  0.34 

—  2.95 

= 

+  1.31 

+  0.90 

96 

—  0.81 

-0.15 

—  1.05 

-1.93 

+  1.83 

+  0.34 

—  0.20 

—  3.87 

= 

+  0.68 

-0.18 

97 

-1.75 

—  0.32 

—  1.47 

—  3.45 

+  2.78 

+  0.51 

-1.00 

—  5.52 

= 

+  2.86 

+  1.13 

98 

-2.47 

—  0.46 

-1.39 

-4.75 

+  3.49 

+  0.65 

-1.61 

—  6.68 

= 

+  2.36 

+  0.02 

99 

-2.10 

-0.39 

—  0.73 

—  4.28 

+  3.12 

+  0.58 

-  1.72 

—  5.98 

= 

+  2.60 

+  0.64 

100 

—  1.05 

-0.20 

-0.11 

—  2.57 

+  2.06 

+  0.38 

-  1.67 

—  3.99 

= 

+  0.79 

—  0.19 

101 

—  0.60 

-0.11 

+  0.02 

-1.85 

+  1.61 

+  0.30 

-1.70 

—  3.02 

= 

+  1.48 

+  0.92 

102 

—  0.35 

—  0.06 

+  0.06 

-  1,47 

+  1.35 

+  0.25 

-1.75 

-2.40 

= 

-0.92 

-1.26 

103 

-  0.0!) 

—  0.02 

+  0.11 

-1.13 

+  1.09 

+  0.20 

-1.82 

-  1.62 

= 

+  0.20 

+  0.12 

101 

+  0.12 

+  0.02 

+  0.09 

+  0.96 

+  0.87 

+  0.17 

—  0.09 

+  2.01 

= 

+  0.46 

+  0.23 

105 

—  0.09 

—  0.02 

-0.10 

+  1.21 

+  1.10 

+  0.22 

+  0.87 

+  2.40 

= 

+  0.79 

+  0.26 

106 

—  0.32 

—  0.06 

—  0.20 

+  1.48 

+  1.31 

+  0.26 

+  1.49 

+  2.60 

— 

+  1.84 

+  0.95 

107 

—  1.21 

—  0.25 

—  0.70 

+  2.84 

+  2.22 

+  0.44 

+  3.45 

+  3.30 

= 

+  5.70 

+  3.37 

108 

—  2.63 

—  0.53 

-2.15 

+  4.76 

+  3.5S 

+  0.72 

+  5.86 

+  4.25 

= 

+  4.49 

-0.01 

109 

-  1.44 

—  0.29 

-1.91 

+  2.58 

+  2.42 

+  0.49 

+  1,11 

+  2.42 

= 

+  3.11 

+  0.51 

110 

—  0.63 

—  0.13 

—  1.27 

+  1.40 

+  1.62 

+  0.33 

+  3.34 

+  1.13 

= 

+  2.10 

+  0.78 

29 


INTRODUCTION. 

Equations  of  condition. 
j^o  Residuals. 


Ill 

__  0.42.r  —  0.09.I/—  1.09;+  1.13»+  1.4Lr'  +  0.29/  +  3.02;'  +  0.72  »'  = 

+  4.67 

+  3.68 

112 

-  0.20 

-0.04 

-  0.92 

+  0.87 

+  1.20 

+  0.2  1 

+  2.65 

+  0.23 

= 

+  1.74 

+  1.08 

113 

+  0.11 

+  0.03 

—  0.76 

+  0.10 

+  O.SG 

+  0.17 

+  1.70 

-  0.82 

= 

+  0.76 

+  0.63 

111 

+  0.2  4 

+  0.05 

—  0.80 

+  0.21 

+  0.75 

+  0.15 

+  1.09 

—  1.20 

= 

+  1.98 

+  2.03 

115 

+  0.39 

+  0.08 

-0.49 

—  0.22 

+  0.08 

+  0.14 

+  0.2  4 

—  1.39 

= 

+  0.96 

+  1.27 

116 

+  0.37 

+  0.08 

—  0.55 

-0.61 

+  0.01 

+  0.13 

—  0,12 

—  1.24 

= 

—  0.50 

—  0.12 

117 

+  0.3S 

+  0.08 

-  0.29 

—  0.77 

+  0.62 

+  0.13 

—  0.77 

—  1.00 

= 

-  1.55 

-  1.11 

118 

+  0.40 

+  0.08 

+  0.15 

—  0.82 

+  0.60 

+  0.12 

-1.07 

—  0.59 

= 

-  '.13 

—  0.63 

119 

+  0,41 

+  0.08 

+  0.33 

—  0.77 

+  0.60 

+  0.12 

-1.16 

—  0.34 

= 

-0.66 

-0.17 

120 

+  0,11 

+  0.09 

+  0.60 

-0.59 

+  0.59 

+  0.12 

—  1.19 

+  0.28 

= 

-2.75 

xJ.27 

121 

+  0.42 

+  0.09 

+  0.81 

-0.23 

+  0.58 

+  0.  12 

—  1.08 

+  0.48 

= 

—  2.23 

-1.81 

122 

+  0.42 

+  0.09 

+  0.84 

+  0.12 

+  0.58 

+  0.12 

—  0.85 

+  0.80 

= 

-0.45 

—  0.09 

123 

+  0.42 

+  0.09 

+  0.43 

+  0.73 

+  0.57 

+  0.12 

—  0.12 

+  1.10 

= 

-0.44 

—  0.21 

124 

+  0.42 

+  0.09 

+  0.22 

+  0.82 

+  0.57 

+  0.  12 

+  0.14 

+  1.16 

= 

—  0.25 

—  0.05 

125 

—  0.62 

—  0.08 

+  1.24 

-1.44 

+  1.63 

+  0.22 

—  3.30 

-1.23 

= 

+  0.50 

—  0.03 

126 

—  1.88 

-0.26 

+  2.98 

—  3.12 

+  2.88 

+  0.39 

-5.80 

—  0.87 

= 

+  0.49 

-1.02 

127 

—  1.65 

-  0.24 

+  3.29 

-1.47 

+  2.65 

+  0.37 

—  5.52 

+  0.04 

= 

+  3.61 

+  2.02 

128 

-0.43 

-0.06 

+  1.57 

—  0.43 

+  1.43 

+  0.20 

-3.07 

+  0.93 

= 

+  0.82 

+  0.31 

12!) 

+  0.18 

+  0.0& 

-0.85 

+  0.36 

+  0.81 

+  0.12 

+  1.70 

+  0.76 

= 

+  0.51 

+  0.43 

130 

+  0.06 

+  0.01 

-1.00 

+  0.24 

+  0.96 

+  0.14 

+  2.18 

+  0.27 

= 

—  0.35 

-  0.56 

131 

-0.15 

—  0.02 

-1.22 

+  0.19 

+  1.15 

+  0.17 

+  2.58 

—  0.38 

= 

+  0.88 

+  0.42 

132 

-0.57 

-0.09 

-1.81 

+  0.19 

+  1.56 

+  0.24 

+  3.19 

—  1.29 

= 

-  1.10 

-  2.05 

133 

-  1.62 

-0.25 

-3.52 

+  0.03 

+  2.67 

+  0,41 

+  4.51 

—  2.92 

= 

+  0.68 

-  1.50 

134 

-2,41 

-0.37 

-4.84 

-0.46 

+  3.57 

+  0.55 

+  5.46 

-4.03 

= 

+  3.34 

+  0.29 

135 

-2.21 

-0.34 

-4.40 

-1.02 

+  3.22 

+  0.49 

+  4.97 

-4.07 

= 

+  1.74 

-0.93 

136 

—  1.18 

-0.18 

—  2.60 

—  0.95 

+  2.18 

+  0.34 

+  3.20 

-3.21 

= 

+  1.44 

0.00 

137 

-0.35 

—  0.05 

-  1.32 

—  0.03 

+  1.36 

+  0.21 

+  1.51 

-2.54 

= 

+  1.09 

+  0.56 

138 

+  0.02 

0.00 

-0.83 

+  0.52 

+  0.97 

+  0.15 

+  0.35 

-2.12 

= 

+  1.32 

+  1.23 

139 

+  0.15 

+  0.03 

+  0.92 

+  0.09 

+  0.84 

+  0.14 

-  1.89 

+  0.22 

= 

-0.60 

-0.59 

140 

-0.07 

—  0.01 

+  1.10 

+  0.35 

+  1.07 

+  0.18 

—  2.09 

+  1.26 

= 

-  0.20 

-  0.50 

141 

-0.30 

—  0.05 

+  1.35 

+  0.52 

+  1.29 

+  0.22 

-2.13 

+  1.99 

= 

+  1.23 

+  0.64 

142 

-1.01 

-0.17 

+  2.28 

+  1.15 

+  2.00 

+  034 

-2.30 

+  3.70 

= 

+  2.00 

+  0.49 

143 

-2.22 

-  0.38 

+  3.80 

+  2.57 

+  3.21 

+  0.54 

—  2.68 

+  6.05 

= 

+  5.49 

+  2.34 

144 

-2.54 

-0.43 

+  3.0(5 

+  3.57 

+  3.51 

+  0.00 

-2.36 

+  6.78 

= 

+  7.55 

+  3.84 

145 

-0.61 

—  0.10 

+  1.02 

+  1.61 

+  1.60 

+  0.27 

-1.65 

+  3.56 

= 

+  3.16 

+  1.98 

146 

+  0.42 

+  0.03 

+  0.30 

+  0.80 

+  0.58 

+  0.05 

+  0.38 

+  1.13 

= 

0.00 

—  0.06 

147 

+  0.41 

+  0.03 

—  0.80 

-  0.24 

+  0.59 

+  0.05 

+  1.02 

-0.58 

= 

-0.11 

+  0.11 

148 

+  0.39 

+  0.03 

-0.04 

-0.83 

+  0.62 

+  0.05 

+  0.06 

-  1.26 

= 

+  1.08 

+  1.40 

149 

+  0.34 

+  0.03 

+  0.56 

-0.61 

+  0.60 

+  0.06 

-0.81 

-  1.12 

= 

-0.51 

-  0.25 

150 

—  0.02 

0.00 

+  0.38 

+  1.00 

+  1.04 

+  0.10 

+  1.03 

+  2.11 

= 

+  0.79 

+  0.40 

151 

+  0.16 

+  0.01 

+  0.12 

+  0.89 

+  0.83 

+  0.08 

+  1,43 

+  1.18 

= 

+  3.21 

+  3.00 

152 

+  0.38 

+  0.04 

—  0.83 

-0.03 

+  0.62 

+  0.06 

+  0.61 

-  1.11 

= 

+  0.34 

+  0.49 

153 

+  0,40 

+  0.04 

-  0.58 

-  0.59 

+  0.00 

+  0.0!) 

-0.13 

-  1.19 

= 

-0.29 

0.00 

151 

+  0.42 

+  0.04 

+  0.06 

+  0.83 

+  0.59 

+  0.08 

-0.83 

-  0.83 

= 

-0.08 

-0.03 

155 

+  0,42 

+  0.0  I 

+  0.72 

+  0,13 

+  0.58 

+  0.06 

-0.81 

+  0.85 

= 

+  1.01 

+  1.21 

30 


INTRODUCTION. 


No. 


Tin'  equations  derived  from  ihc  latitudes  »;  contain  two  more  unknown  quantities, 

v  =  J  ?'         ,  to  =  sin  t'.  -I  Q', 

lint  in  them  tlic  variation  ol'tlic  solar  elements  will  be  neglected. 
Tlio  mean  oflhe  Transits  of  17(il  and  17(59  gives 

-0.059  x  +  0.050 //   —0.095:   —  0.069  u  +  0.00  v   +  1.000  w  =  —  I".  165. 
From  tins  mean  the  indeterminate  correction  of  the  Sun's  semi-diameter  is  nearly  eliminated. 

Equations  of  condition. 


No. 

H 

1 

-  0.01* 

+  0.000 

-  0.0  Iz 

+  0.00« 

+ 

0.6  lv 

+  1.24w 

=    + 

0.82 

2 

-0.10 

+  0.01 

-0.21 

-0.08 

— 

0.36 

+  1.95 

=    + 

0.41 

3 

-  0.12 

+  0.02 

-0.31 

-0.11 

— 

1.09 

+  2.04 

=   — 

0.49 

4 

+  0.17 

-0.02 

-0.41 

+  0.25 

— 

2.13 

+  0.88 

=     

0.14 

5 

+  0.20 

-0.03 

-0.37 

+  0.17 

— 

.1.60 

-  0.40 

=     — 

1.51 

6 

+  0.09 

-  0.01 

-  0.14 

—  0.10 

+ 

0.12 

-  1.35 

=      + 

0.02 

7 

+  0.20 

-  0.02 

-  0.23 

-  0.35 

+ 

1.17 

-  1,12 

=      + 

5.62 

8 

+  0.19 

-  0.02 

-0.30 

-0.49 

+ 

2.32 

-0.77 

=      + 

1.51 

9 

-0.14 

+  0.02 

-  0.51 

-0.16 

+ 

2.12 

+  0.46 

=     + 

0.64 

10 

-0.23 

+  0.03 

-0.54 

-  0.07 

+ 

1.88 

+  1.10 

=     — 

1.70 

11 

-  0.18 

+  0.02 

-0.36 

-0.10 

+ 

1.05 

+  1.38 

1.48 

12 

-  0.22 

+  0.02 

-  0.01 

-  0.58 

— 

2.3  1 

-0.09 

=          

1.49 

13 

+  0.11 

-0.01 

-  0.33 

-  0.36 

— 

2.06 

-   1.55 

=      + 

1.04 

14 

+  0.12 

-0.01 

+  0.21 

-0.24 

+ 

1.57 

+  1.68 

=      + 

0.31 

15 

-  0.03 

0.00 

-  0.02 

-  0.0!) 

+ 

0.06 

+  2.31 

=      + 

0.63 

31 

156 

4-0.  i\.i 

•4-  0.0  [it     0.25*      0.81»4-0.69a 

•>  4-  0.064 

,/_o.ioy  4-  i.2iH'=  4- 

0.38 

4-0.75 

157 

4-0.3!) 

4-  o.o  i 

—  0,11 

4-  0.72 

4-  0.60 

4-0.06 

4-  0.65 

4-  i.os 

=  — 

0.61 

—  0.57 

158 

4-  0.35 

4-0.01 

-  0,s:, 

4-0.01 

4-  0.65 

4-0.07 

4-  1.38 

4-  0.2  1 

=  — 

1.16 

-  1.04 

159 

4-0.1!) 

4-  0.02 

-0.61 

-  O.(i5 

4-0.81 

4-  o.08 

4-  1.26 

-  1.29 

=  — 

0.19 

-  0.07 

160 

4-0.21 

4-  0.02 

-)-  0.35 

—  0.80 

4-0.77 

4-  0.08 

-  1.76 

-0.15 

=  4- 

i..-,o 

4-  1.69 

161 

4-  0.3  1 

4-0.01 

4-o.Ni 

0.21 

4-  0.66 

4-0.07 

-O.iM 

4-  1.06 

=  — 

0.53 

—  0.30 

162 

4-o.:ii 

4-  0.06 

0.63 

4-  0.52 

4-  0.66 

4-0.11 

4-  1.25 

—  0.55 

1 

1.72 

4-  1.80 

163 

4-  0.3S 

4-  0.07 

-  0.82 

-  0.05 

4-  0.62 

4-  o.  1  1 

4-0.60 

-  1.10 

=  + 

0.98 

4-  1.22 

161 

4-  o.  12 

4-  0.07 

-  0.02 

0.85 

4-  0.59 

4-0.10 

-  O.7.") 

-  0.90 

=  — 

0.97 

-  0.50 

165 

4-  o.  12 

4-0.07 

4-  O.S3 

—  0.13 

4-  0.5S 

4-0.10 

-  1.13 

4-  0.28 

=  4- 

0.52 

4-  0.89 

166 

4-  o.  1  1 

4-0.07 

4-  0.6  1 

4-  0.55 

4-  0.58 

4-0.10 

-0.70 

4-  0.!)5 

=  4-0.01 

4-0.24 

167 

4-0.17 

4-  0.03 

4-  0.2!) 

-  O.N5 

4-  O.S3 

4-0.16 

-  1.81 

-  0.  13 

=  4- 

1.38 

4-  1.57 

168 

4-  0.35 

4-  0.07 

4-  0.82 

-  0.  10 

4-  0.65 

4-0.12 

-  1.16 

-f-0.75 

=  4- 

0.61 

4-0.90 

16!) 

4-  0.38 

4-  0.07 

4-  0.75 

4-  0.38 

4-0.61 

4-0.12 

—  0.07 

4-  1.29 

=  + 

0.85 

4-  1.09 

170 

4-  0.  12 

4-  0.08 

-  0.7!) 

4-  0.24 

4-0.58 

4-0.11 

4-  1.10 

—  0.35 

=  — 

0.73 

-0.48 

m 

4-  o.  12 

4-0.08 

—  0.35 

-0.76 

4-  0.5!) 

4-o.li 

4-0.18 

-  1.15 

=  — 

0.27 

4-  0.20 

17--' 

4-  o.  12 

4-0.08 

4-0.27 

-0.81 

4-  0.58 

4-  o.  1  1 

-0.50 

-  1.05 

=  — 

3.06 

—  2.55 

173 

4-  0.3S 

4-0.07 

4-0.79 

-  0.27 

4-  0.62 

4-0.12 

-  1.27 

-0.50 

=  — 

0.26 

4-0.10 

11  1 

4-0.31 

4-0.06 

4-0.81 

4  0.20 

4-  0.6  I 

4-0.13 

-  1.35 

4-0.18 

=  — 

2.86 

—  2.65 

L75 

4-  0.32 

4-  o.oe 

4-  0.65 

4-  0.55 

4-0.68 

4-0.13 

—  1.25 

4-0.80 

=  — 

0.73 

—  0.60 

No. 


INTRODUCTION. 


Equations  of  condition. 


// 

16 

+  0.02x 

O.OOy 

+  0.01% 

+  O.OSw 

-  0.75i. 

+  1.69w 

=  -0.77 

17 

+  0.01 

0.00 

-  0.07 

+  0.04 

+  0.27 

-2.68 

=  +  2.21 

18 

-0.15 

+  0.01 

-0.12 

+  0.32 

+  1.60 

—  1.45 

=  +  0.21 

19 

+  0.01 

0.00 

+  0.02 

0.00 

+  0.78 

+  0.97 

=  +  1.13 

20 

+  0.10 

0.00 

—  0.38 

+  0.18 

-2.05 

+  1.36 

=  -  0.77 

21 

+  0.11 

0.00 

-0.17 

-  0.11 

+  0.33 

-  1.45 

=  +  0.53 

22 

+  0.23 

-0.01 

—  0.28 

-0.45 

+  1.G3 

-  1.35 

=  +  0.73 

23 

-  0.23 

+  0.01 

-  0.57 

—  0.06 

+  2.13 

+  0.86 

-  1.07 

24 

-  0.13 

0.00 

—  0.12 

—  0.25 

-  0.86 

+  1.09 

=  +  0.95 

25 

—  0.17 

0.00 

—  0.07 

-0.56 

-  2.43 

-  0.35 

=  -  0.67 

26 

+  0.07 

0.00 

-  0.09 

-  0.11 

+  0.09 

—  1.54 

=  +  0.53 

27 

+  0.10 

0.00 

+  0.18 

-  0.2  1 

+  1.52 

+  1.83 

=  -  0.65 

1 

28 

+  0.01 

0.00 

0.00 

+  0.02 

-  0.62 

+  1.79 

=  +  3.82 

29 

-0.06 

0.00 

+  0.14 

-0.05 

-  1.03 

-  1.91 

=  —  2.56 

30 

0.00 

0.00 

-0.07 

+  0.07 

+  0.49 

-  2.67 

=  -  0.52 

31 

—  0.15 

0.00 

-  0.15 

+  0.29 

+  1.60 

-  0.73 

=  -  0.13 

32 

-  0.10 

0.00 

—  0.30 

-0.06 

-  1.04 

+  2.13 

==  +  0.55 

33 

+  0.21 

+  0.01 

-0.38 

+  0.27 

-  1.92 

+  0.18 

=  -  0.52 

34 

+  0.16 

0.00 

-0.30 

+  0.10 

-  1.27 

-  0.63 

=  -  0.79 

35 

+  0.14 

+  0.01 

-  0.21 

-  0.20 

+  0.59 

-  1.51 

=  -  0.38 

36 

+  0.22 

+  0.01 

-0.27 

-0.39 

+  1.41 

-  1.47 

=  +  1.29 

37 

+  0.16 

+  0.01 

-0.37 

-  0.44 

+  2.39 

-0.81 

=  -  0.72 

38 

-0.16 

-0.01 

-  0.12 

-0.30 

-0.98 

+  1.12 

=  +  0.33 

39 

-  0.18 

—  0.01 

-0.09 

-  0.56 

-2.43 

-  0.21 

=  +  2.84 

40 

+  0.17 

+  0.01 

-0.42 

—  0.29 

-  1.88 

-  1.59 

=  -  1.00 

41 

+  0.06 

0.00 

-0.08 

-  0.10 

+  0.20 

-  1.44 

=  +  0.10 

42 

+  0.06 

0.00 

-0.06 

-  0.11 

+  031 

-  0.86 

=  +  0.03 

43 

+  0.13 

+  0.01 

+  0.04 

-0.25 

+  1.18 

-  0.46 

=  +  0.64 

44 

+  0.18 

+  0.01 

+  0.22 

-  0.32 

+  1.78 

+  0.86 

=  -  0.92 

45 

-0.05 

0.00 

-  0.03 

-0.14 

+  0.33 

+  2.36 

=  -  0.04 

46 

+  0.02 

0.00 

+  0.01 

+  0.05 

—  0.80 

+  1.48 

=  +  0.66 

47 

+  0.05 

0.00 

—  0.01 

+  0.10 

-  1.04 

+  0.90 

=  +  0.64 

48 

—  0.03 

0.00 

-0.05 

—  0.05 

+  0.03 

+  0.70 

=  +  0.07 

49 

-  0.07 

-0.01 

-0.02 

-0.13 

-  0.68 

+  0.61 

=  -  1.75 

50 

-0.09 

—  0.01 

+  0.09 

-  0.16 

—  1.15 

+  0.14 

=  -  0.90 

51 

—  0.11 

-0.01 

+  0.19 

-  0.12 

-  1.37 

—  1.06 

=  -  3.16 

52 

-0.03 

0.00 

+  0.09 

-  0.03 

—  0.71 

-  2.35 

-  4.41 

53 

-  0.03 

0.00 

-0.07 

+  0.13 

+  0.84 

—  2.49 

=  —  1.78 

51 

-  0.14 

-  0.01 

-  0.10 

+  0.29 

+  1.54 

—  1.26 

=  +  3.67 

55 

-  0.12 

-0.01 

-  0.14 

+  0.19 

+  1.45 

-  0.21 

=  +  0.35 

56 

+  0.04 

0.00 

+  0.06 

-0.05 

+  0.93 

+  0.14 

=  +  1.39 

57 

+  0.03 

0.00 

+  0.05 

-  0.02 

+  0.90 

+  0.79 

=  +  1.57 

58 

-0.05 

0.00 

—  0.10 

-  0.02 

+  0.18 

+  1.80 

=  +2.67 

59 

-0.08 

—  0.01 

-  0.30 

—  0.03 

-  1.11 

+  2.13 

=  +  2.72 

60 

+  0.16 

+  0.02 

—  0.31 

+  0.13 

—  1.37 

—  0.50 

=  +  0.58 

32 

No. 


INTRODUCTION. 

iif  riin/liliiin. 


61 

4-  O.I  Or 

4-  0.01// 

-0.19; 

-  0.01  it 

—  0.63r 

-  O.'IOrc    = 

-  0.01 

69 

0.00 

0.00 

—  0.01 

0.00 

— 

0.70 

-  0.73       = 

-  1.35 

63 

4-  0.0  1 

D.OD 

-0.07 

— 

0.02 

— 

0.37 

4- 

1.15 

= 

-  1.50 

61 

4-  0.13 

4-  0.01 

-  0.20 

— 

0.17 

4 

0.11 

-  1.54       = 

-  0.74 

65 

4-  0.22 

4-  0.03 

-  0.3  1 

— 

0.17 

+ 

2.01 

-  1.19       = 

-  3.3S 

66 

—  0.-2  I 

—  0.03 

—  0.59 

— 

0.02 

4- 

2.26 

+ 

0.54 

= 

4-  2,16 

67 

—  0.0s 

—  0.01 

-  0.14 

— 

0.09 

f 

0.1(1 

f. 

1.2.') 

mm 

-0.29 

6S 

—  0.03 

0.00 

-0.03 

— 

().().-, 

— 

0.  10 

+ 

0.89 

= 

4-  3.00 

69 

-0.01 

0.00 

—  0.07 

— 

0.03 

+ 

0.2(i 

f 

0.90 

= 

4-  0.62 

70 

—  0.07 

-0.01 

—  0.09 

— 

0.11 

— 

0.36 

4 

1.15 

= 

-2.16 

71 

-0.11 

—  0.02 

-  0.13 

— 

0.2.-. 

— 

0.80 

4- 

1.15 

— 

-  3.21 

72 

-  0.23 

—  0.03 

-  0.07 

— 

0.49 

— 

1.74 

4- 

0.76 

= 

—  0.32 

73 

-0.17 

—  0.02 

-  0.12 

— 

o..-.(  ; 

— 

2.41 

— 

0.21 

= 

4-  2.  10 

71 

4-  0.16 

4-  0.02 

—  0.2s 

— 

0.18 

— 

0.74 

— 

1.75 

= 

-  2.59 

75 

4-0.04 

4-  0.01 

—  0.05 

— 

0.07 

+ 

0.33 

— 

1.30 

= 

-0.70 

76 

4-0.06 

4-0.01 

-0.07 

— 

0.10 

+ 

0.26 

— 

0.86 

= 

-0.80 

77 

4-  0.16 

4-  0.02 

4-0.09 

— 

0.30 

4- 

1.13 

— 

0.21 

= 

4-0.69 

78 

4-0.19 

4-  0.03 

4-  0.21 

— 

0.31 

4- 

1.75 

4- 

0.50 

= 

4-  0.68 

79 

4-  0.13 

4-  0.02 

+  0.20 

— 

0.30 

4- 

1.72 

+ 

1.54 

= 

-0.50 

80 

4-  0.01 

0.00 

4-  0.03 

— 

0.17 

4- 

1.22 

4- 

2.20 

= 

4-  0,45 

81 

-0.01 

—  0.01 

-  0.03 

— 

0.09 

4- 

0.07 

4. 

2.22 



4-  0.26 

82 

4-  0.02 

0.00 

4-0.01 

4- 

0.01 

— 

0.76 

4- 

1.50 

= 

—  0.82 

83 

4-  0.04 

4-  0.01 

0.00 

4- 

o.os 

— 

0.99 

+ 

1.02 

= 

-0.72 

SI 

4-  O.or. 

4-  0.01 

-  0.01 

4- 

0.10 

— 

1.06 

+ 

0.30 

= 

-0.07 

85 

-  O.OS 

-0.01 

4-  0.01 

— 

0.16 

— 

0.88 

+ 

0.49 

= 

4-  O.H3 

86 

-0.11 

-  0.02 

4-  0.12 

— 

0.17 

— 

1.29 



0.09 

—  - 

—  1.35 

87 

-  0.12 

-0.02 

4-  0.17 

— 

0.16 

— 

1.41 

— 

0.56 

= 

4-  0,15 

88 

—  0.10 

—  0.02 

4-  0.20 

— 

0.09 

— 

1.26 

— 

1.63 

= 

-0.07 

89 

-  0.03 

0.00 

4-0.07 

— 

0.04 

— 

0.61 

— 

2.49 

= 

4-  0.5S 

90 

-0.09 

—  0.02 

-0.05 

4- 

0.23 

4- 

1.23 

— 

2.00 

= 

4-  1.11 

91 

—  0.11 

—  0.02 

-0.17 

4- 

0.15 

4- 

1.24 

4- 

0.17 

= 

4-  0.70 

92 

-0.01 

-0.01 

—  0.07 

— 

0.03 

4- 

0.01 

+ 

0.75 

— 

-  O.I!) 

93 

4-0.01 

4-0.01 

4-0.06 

— 

0.05 

4- 

0.96 

4- 

0.26 

= 

4-  O.N3 

94 

4-  0.03 

4-  0.01 

4-  0.06 

— 

0.02 

+ 

0.95 

4- 

0.6!) 

= 

4-  0.99 

95 

4-0.02 

0.00 

4-  0.0  1 

— 

0.01 

+ 

0.82 

4- 

1.06 

= 

4-  0.89 

96 

-0.02 

0.00 

—  0.04 

0.00 

4- 

0.44 

4- 

1.61 

— 

4-  0.92 

97 

-0.09 

-  0.02 

-0.21 

— 

0.05 

— 

on 

-f 

2.14 

^ 

4-  0.44 

98 

-  0.03 

0.00 

-0.31 

4- 

0.05 

— 

i.ii 

| 

2.02 

= 

4-  1.56 

99 

4-  0.14 

4-0.03 

—  0.33 

+ 

0.27 

— 

1.96 

4- 

1.25 

= 

-  1.15 

100 

4-  0.20 

4-  0.01 

-  0.3  1 

4- 

0.26 

— 

1.79 

4- 

0.12 

= 

-0.91 

101 

4-  0.17 

4-  0.03 

—  0.31 

4- 

0.17 

— 

1.48 

— 

0.35 

= 

4-  0.19 

102 

4-0.14 

4-  0.03 

-  0.27 

4- 

0.09 

— 

1.18 

— 

0.62 

= 

—  0.52 

103 

4-0.10 

4-  0.02 

-  0.20 

0.00 

— 

0.72 

— 

O.S6 

= 

-0.60 

104 

—  Q.01 

0.00 

4-  0.01 

0.00 

— 

0.79 

— 

0.52 

= 

+  0.02 

105 

4-  0.03 

4-0.01 

—  0.06 

— 

0.01 

— 

0.  13 

— 

1.12 

= 

4-  0.74 

5V 

33 

No. 


INTRODUCTION 


Iniiulionfs  of  condition. 


106 

+  0.07* 

+  0.01/y 

—  0.13; 

—  0.06« 

-  O.OSy 

-  1.38(0 

=  +  1.18 

107 

+  0.20 

+  0.04 

—  0.28 

-0.33 

+  1.14 

—  1.61 

=  +  0.54 

108 

+  0.05 

+  0.01 

—  0.46 

—  0.30 

+  2.47 

-  0.62 

=  +  0.96 

109 

-  0.24 

—  0.05 

—  0.53 

0.00 

+  1.77 

+  0.94 

=  +  0.22 

110 

—  0.16 

—  0.03 

-  0.31 

—  0.07 

+  0.88 

+  1.27 

=  +  1.94 

111 

-0.12 

—  0.02 

—  0.23 

—  0.09 

+  0.56 

+  1.28 

=  +  1.03 

112 

—  0.08 

—  0.02 

—  0.14 

-0.09 

+  0.16 

+  1.20 

=  +  1.81 

113 

-0.01 

0.00 

—  0.01 

—  0.03 

—  0.57 

+  0.65 

=  ;-  0.34 

125 

—  0.17 

—  0.02 

—  0.12 

-0.33 

-  1.12 

-f  1.08 

=  +  1.69 

126 

-  0.23 

—  0.03 

-  0.07 

-  0.49 

-  2.24 

+  0.23 

=  +  1.42 

127 

+  0.19 

+  0.03 

-  0.39 

—  0.22 

-  1.30 

-  1.73 

=  +  0.59 

128 

+  0.06 

+  0.01 

—  0.08 

—  0.10 

+  0.16 

—  1.43 

=  +  0.76 

J29 

+  0.05 

+  0.01 

-0.07 

-0.08 

+  0.11 

-0.85 

=  -  0.11 

130 

+  0.08 

+  0.01 

-0.05 

—  0.16 

+  0.56 

—  0.85 

=  +  0.64 

131 

+  0.12 

+  0.02 

+  0.01 

—  0.2  1 

+  1.03 

—  0.61 

=  +  0.74 

132 

+  0.17 

+  0.02 

+  0.12 

—  0.31 

+  1.51 

—  0.08 

=  +  1.60 

133 

+  0.18 

+  0.03 

+  0.24 

-  0.33 

+  1.81 

+  1.08 

=  +  1.68 

134 

+  0.07 

+  0.01 

+  0.13 

-  0.29 

+  1.47 

+  1.98 

=  -0.50 

135 

-0.06 

—  0.01 

-0.05 

—  0.18 

+  0.46 

+  2.34 

=  +  0.90 

136 

-0.01 

0.00 

0.00 

—  0.01 

-  0.51 

+  1.80 

=  —  0.11 

137 

+  0.05 

+  0.01 

-  0.01 

+  0.09 

-  1.03 

+  0.84 

=  -  0.35 

138 

+  0.05 

+  0.01 

-0.06 

+  0.09 

-  0.99 

+  0.03 

=  +  0.88 

139 

-0.06 

-0.01 

—  0.02 

-0.12 

-0.56 

+  0.66 

=  -0.91 

140 

-0.09 

—  0.02 

+  0.07 

-0.17 

-  1.13 

+  0.23 

=  -0.84 

141 

-0.11 

-  0.02 

+  0.14 

-0.17 

-  1.34 

—  0.22 

-  1.90 

142 

-0.11 

-  0.02 

+  0.21 

-0.11 

-  1.37 

-  1.26 

=  —  1.37 

143 

-0.04 

—  0.01 

+  0.11 

-0.05 

-0.77 

—  2.38 

=  -0.65 

144 

-0.03 

-0.01 

-0.05 

+  0.12 

+  0.77 

-2.51 

=  +  3.52 

145 

—  0.14 

-  0.02 

—  0.14 

+  0.24 

+  1.48 

-  0.50 

=  +  0.28 

To  apply  to  these  equations  the  rigorous  method  of  least  squares  would  be  very  laborious:  hence  a  method 
of  "  Equivalent  Factors"  has  been  used;  the  equations  have  been  multiplied  either  by.  whole  numbers  or  by  frac- 
tions which  are  ready  multipliers.  In  this  way,  the  following  Normal  Equations  were  derived  from  tho  equations 
of  condition  which  have  cos  ij.  A  0  for  their  absolute  terms, 

// 

+  195.841-  — 44.809y  +  127.71z  +  73.19;t  —251.90^  +  43.027/  —  85.48;' +  119.25u'  =-  8.77 
_  44.78  +47.099  -  83.68  —  62.84  +  41.04  —48.460  +  41.17  -  96.06  =  —113.43 
+  120.94  —83.889  +427.28  +133.17  -136.59  +82.936  -410.76  +400-15  =  +162.30 
+  70.03  —62.965  +135.64  +365.81  -  73.13  +63.350  +114.76  +508.04  =  +197.06 

—255.15     +42.172      -138.12       -  80.06     +125.64  —27.182  +   91.22  —132.67  =  +   92.63 

+  40.68      -48.373     +   82.84     +   61.99       -  26.27  +51.815  -  41.45  +   94.13  =  +121.18 

-  83.42     +41.537      -422.53     +119.76     +102.83  —40.091  +644.06  -111.82  =  —  23.87 

+  112.81     —95.792     +406.68     +505.65      -126.69  +94.621  —120.34  +902.21  =  +264.18 

34 


I  NTKODUCTION. 


It'  ii    is  eliminated  IVoin  these  equations,  tin'  result  is 


+ 

L81.8& 

-32.2130     +100.57: 

-237.  27.' 

+  30.352//'    —108 

.11-.'    +    17.60«'    =  - 

IS.'-JO 

— 

+  36.\!s  1          -   6().:{s 

+   28.  |s 

-37.577 

+   60.  ss 

—      8.78         =   — 

+ 

95.  15 

-60.971        +377.!)0 

—  109.H7 

|  59.  si  1 

-452.54 

+  215.20        = 

+ 

90.5:; 

—  281 

+  28.391       —ION.  13 

+  109.63 

-13.317 

+  116.31 

-  21. 

18 

- 

+ 

135.K; 

+ 

28.81 

-37.705        4-    59.N5 

-    13.ss 

+  11.  Os() 

-   60.90 

+     8.04       = 

4- 

— 

106.35 

!  1  17        —466.91 

+  126.77 

—60.831 

+  606. 

111 

—278.15        =  — 

88.88 

+ 

16.01 

_   s.770        +219.  IS 

-   25.60 

+   7.0r>3 

-27S.91 

+  199.94       =  — 

And  if  from  tip                   liminated.  the  result  is 

+  156.13.C        -15.9S7//        —  20S.OO.C'       +14 

.US,/' 

+  11.99.:' 

-39.67"' 

// 
=  -   72.30 

—    17 

.50         +26.512         + 

1091          —28 

.055 

-11.42 

+25.60 

= 

— 

G5 

.11 

—  212,13          +10.900          +378.0S          +   3 

.863 

-13.51 

+  10.27 

= 

+ 

161 

.74 

+    13 

.6!)          -28.019          + 

3.51         +31 

.598 

+  10.77 

-26.01 

= 

+ 

73.  15 

+    U 

.59         -13.190 

9.11         +13 

.151 

+47.33 

—  12.25 

= 

i- 

23 

.52 

-  39 

.35         +26.593         + 

38.18         -27.674 

-16.50 

+75.13 

= 

— 

61 

.46 

It  is  evident  now,  that  since  the  principal  co-efficients  of:'  and  u'  have  fallen  from  <>  1  1.06  and  902.21  to  i7.33 
and  75.13,  no  very  reliable  values  of  these  quantities  can  he  obtained  from  these  equations.  The  elimination  ol 
//  gives 


+  145.89J' 

—  201.13.1' 

-  2.1SO//' 

+    5.112' 

—  24.25w' 

=  —111.52 

-205.2  1 

+  373.60 

+  15.384 

-  8.82 

+29.76 

=  +188.48 

-     4.80 

-    15.07 

+    1.950 

-   1.30 

-   1.01 

=  +     4.64 

+     2.89 

-     3.69 

-  0.791 

+41.65 

+   0.47 

=  -     8.84 

-  21.82 

+  27.25 

+   0.435 

-  5.06 

+49.48 

=  +     3.78 

The  elimination  of  #  from  these  gives 


+  90.23^  +11.895)/'  —    1.63;' 

+  8.11  +    1.868  —   1.13 

+  0.30  -  0.742  +41.55 

—  2.88  +  O.Ofil  —  4.30 


-  4.35«' 
+  0.21 
+  0.95 
+45.85 


=  +31.63 
=  +  0.97 
=  -  G.63 
=  -12.89 


The  elimination  of  x'  from  these  gives 


+0.755//'  -  0.98.Z'  +  0.62w'  =  -  1.99 
—0.782  +41.56  +  0.96  =  —  6.74 
+0.444  -  4.35  +45.71  =  -11.88 

The  only  condition,  relative  to  the  solar  elements,  which  can  be  obtained  with  any  weight,  from  these  equa- 
tions, is 

x1  +  0.132  \f  —  +  0".335. 

That  is,  the  mean  longitude  of  the  Sun  of  HANSEN  and  OLUFSEN'S  Tables  ought  to  be  increased  by  a  third  of  a 
second  at  the  epoch  1863.  As,  however,  these  Tables  will,  probably,  be  used,  for  a  long  time  to  come,  in  rom- 
puting  the  solar  eo<'irdinatfs  of  the  Amrricitu  l:'ji/n'mi'ria,  i/',  ~J  and  it'  will  be  put  severally  equal  to  zero;  and  as 
it  lias  been  decided  to  use  the  1'ulkova  constant  of  aberration,  ,r'  will  he  put  equal  to  +  0".19.  With  these 
assumptions,  the  values  of  x,  y,  z  and  «  are 

-  0".502,     //  =  -  2".N63,     z  =  -  0".040,     u  =  +  0".195. 

The  equation  of  condition  derived  from  the  Transits  of  1761  and  1769  being  excluded,  the  normal  equations, 
determining  the  corrections  of  the  inclination  and  the  longitude  of  the  ascending  node,  are 

+  2.51  x  +  0.390  y  +  1.84  s  -  0.67  u  +  163.26  v  -      0,42  w     =  +  26".(>2 
-1,16      -0.105       -(V»)        -1.06      -      5.86      +188.58        =  +  24.11 

35 


INTRODUCTION. 

From  these  arc  obtained  tlie  following  values  of  o  and  w. 

v  =  +  0".18Z     w  =  +  0".12  or  J  Q'  ==  +  2".0. 

But  from  the  equation  furnished  by  the  Transits  in  1761  and  17(59, 

J  8'  =  -  17".84. 

If  the  first  result  is  suppose,!  to  belong  to  1855.0,  and  the  second  to  1765.4,  the  proper  value  of  the  correction  is 

J  Q'  =  +  0".9  +  W2-J2  I. 

The  origin  of  the  pretty  large  correction  —  0".02863,  of  the  mean  motion  of  Venus,  is  easily  shown.     In  his 
investigation,  LEVEKKIKK  (Ainin/m,  Vol.  VI.,  p.  72)  found  the  following  value  of  J  «', 
J  n'  =  +  0".00085  +  0".0689  v  +  0".0959  >'  +  0".1207  /'; 

but  the  value  of  this  quantity  used  in  forming  his  Tables  is  the  first  term  only.  If  the  values  of  v,  v1  and  /'  cor- 
responding to  the  change  from  LEVERRIER'S  values  of  the  masses  to  those  here  adopted,  be  substituted  in  this 
expression,  the  correction  of  LEVERRIER'S  mean  motion,  from  this  cause,  is  found  to  be 

J  «.'  =  —  0".01588. 

Moreover,  a  comparison  of  the  values  of  the  Sun's  mean  longitude  in  the  Tables  of  HANSEN  and  OLUFSEN  and 
of  LEVERRIER,  gives 

Han.  -  Lev.  =  -  0".93  -  0".01074  t. 

From  the  way  in  which  J  n'  and  J  n"  are  involved  in  the  equations  of  condition,  it  may  be  concluded,  that 
if  J  n"  were  left  indeterminate  in  the  solution,  the  value  of  A  n',  obtained,  would  be  roughly, 

J«'  =  (J«')  +  1.2  J  «", 

(J  n')  denoting  the  value  of  J  n'  on  the  supposition  of  J  n"  =  0.  Thus  on  making  J  n"  =  —  0".01074,  the  cor- 
rection of  the  mean  motion  of  Venus,  from  this  cause  is 

J  «'  =  —  0".01289. 
The  sum  of  these  two  corrections  is 

J  n'  =  —  0".02877 

which  is  almost  identical  with  that  derived  from  the  equations  of  condition. 

The  increment  of  the  motion  of  the  node,  0".222,  requires  that  the  mass  of  Venus  should  be  reduced  from 

408134  to  4-J7-MO'  '^'1's  a§l'ees  w*t'1  LEVERRIER'S  result:  setting  out  with  the  mass  0.0000024885,  he  found  that  it 
should  be  multiplex!  by  the  factor  0.948,  which  would  make  the  mass  ij 


The  corrections  to  be  added  to  the  elements,  with  which  we  set  out,  to  obtain  the  elements,  from  which  the 
Tables  are  constructed,  are 

J   L'  =  —    0".502, 

A    -'  =  +  28".46, 

A  Q'  =  +    0".90    +0".222«, 

A    V  =  +    0".18, 

A    e'  =  -     0.000000196, 

J    n'  =  —    0".02863. 

The  Tables  have  been  compared  with  the  occultation  of  Mercury  by  Venus,  observed  at  Greenwich  May  28, 
1737.     The  observations  made  are 

Greenwich  M.  T. 

h       m       6 

9  40     3.9.          Mercury  distant  from  Venus  not  more  than  a  tenth  part  of  the  diameter  of  Venus. 
9  48   10.2.          Mercury  wholly  occulted  by  Venus. 

36 


I  XTRODUCTION. 

The  position  of  Mercury  heiut;  derived  from  1'rof.  WINLOCK'S  '1'ables,  the  apparent  position  of  the  two  planets, 
as  seen  from  (Irecnwich,  and  in  longitude  and  latitude,  are 

<;r-,.,,wirh  M.T.  /.  I.  /'.  //.  I'— I.  b'—l,' 

d  ll  Q  I  It  O  I  f  Q  I  II  Q  I  It  II  II 

Ma>  2S     H         Mi  21   2:U>:>     +2     !)    12.90     89  :M   -19.97     4-210     9.98     4-11(5.92     +  5'/.OS 

10       M)  :U  :«).:!.">    4-2    8  r.s.r.i    M»  :i<)  :w.<;:!    4-29  l  l.2s          50.72    4-15.85 

And  interpolating 

(ii.  -i-iiw  ii-li  .M.  T.  /'  —  /.  //  —  li.  Out.  of  Centres. 

ll         III  8  //  //  // 

9  10    :{.«>  4-  :n.T.1  +  22.(il  :w.9<i 

!)    is    10.2  1.79  4-  19.87  19.95 

With  the  addition  of  0".;">7  for  irradiation,  the  semi-diameters  of  Mercury  and  Venus  are  respectively  .'{".98 
and  2(i".97  :  hence  at  the  first  observation,  the  distance  of  the  limbs  of  the  planet  is  IS". 01,  2".G  more  than  a  lenth 
part  of  the  diameter  of  Venus:  at  the  second  observation,  the  distance  of  the  centres  is  less  than  the  dill'ereiice  of 
semi-diameters;  hence  the  Tables  are  verified  by  the  statement  of  the  observer.  Venus  beinjr,  at  the  time,  a  thin 
Crescent,  and  about  half  of  Mercury's  disc  being  illuminated,  it  is  plain  that  it  would  be  difficult  for  the  obsever 
.o  estimate-  the  distance  in  fractional  parts  of  the  apparent  diameter  of  Venus. 

LEVKKKIEH'S  remarks  on  this  occultatton  are  impaired  by  a  mistake  made  in  the  last  line  of  his  computatk  n. 


37 


TABLES  OF  VENUS. 


TABLE  1. 


LONGITUDE  OF  THE  PRINCIPAL  OBSERVATORIES  FROM  WASHINGTON. 

West  Longitudes  are  marked  + 

Place. 

Longitude 
from  VVashingtoi 
in  Time. 

In  Decimals 
of  a  Day. 

Place. 

Longitude 
from  Washington 
in  Time. 

In  Decimals 
of  a  Day. 

Abo, 

h      m        s 

—6  37  20.32 

—0.2759296 

Lcipsic, 

h      m       s 

—  5  57  46.87 

—  o!2484592 

Albany,* 

—0  13  12.87 

—0.0091767 

Leyden, 

-  5  26     8.57 

—0.2264881 

Allegheny,* 

-fO  11  50.20 

+0.0082199 

Liverpool, 

—  4  56  ]-.'.;{  1 

—0.2056984 

Altona, 

—5  47  58.54 

—0.2416498 

Madras, 

—10  29     9.67 

—0.1369175 

Ann  Arbor, 

+0  26  42.67 

+0.0185494 

Madrid, 

—  4  53  27.00 

—0.2037847 

Armagh, 

—4  41  36.92 

—0.1955662 

Mannheim, 

-  5  42     3.06 

—0.2375354 

Athens, 

—6  43    7.58 

—0.2799488 

Markree, 

-  4  34  24.00 

—0.1905556 

Berlin, 

—6     1  47.77 

—0.2512473 

Marseilles, 

-  5  29  40.55 

—0.2289415 

Bilk, 

—5  35  17.77 

—0.2328445 

Melbourne, 

—14  48     7.17 

—0.6167496 

Bonn, 

—5  36  36.02 

—0.2337502 

Milan, 

-  5  44  58.20 

—0.2395625 

Breslau, 

—6  16  22.19 

—0.2613679 

Modena, 

-  5  51  55.53 

—0.2443927 

Brussels, 

—5  25  41.29 

—0.2261723 

Moscow, 

—  7  38  29.29 

—0.3183946 

Cambridge,  (Eng.) 

—5    8  35.08 

—0.2)42949 

Munich, 

—  5  54  38.00 

—0.2462731 

Cambridge,  (Mass.) 

—0  23  41.54 

—0.0164530 

Naples, 

-  6     5  10.95 

—0.2535990 

Cape  of  Good  Hope, 

—6  22    8.09 

—0.2653711 

New  York,* 

-  0  12  15.47 

—0.0085124 

Chicago, 

+0  42  14.26 

+0.0293317 

Nicolajcw, 

—  7  16     6.53 

—0.3028534 

Cincinnati,* 

+0  29  46.94 

+0.0206822 

Olmiitz, 

—  6  17  15.43 

—0.2519841 

Christiania, 

—5  51     6.69 

—0.2438274 

Oxford, 

—  5     3     9.79 

—0.2105300 

Clinton, 

—0     6  35.08 

—0.0015727 

Padua, 

-  5  55  41.17 

—0.2470013 

Copenhagen, 

—5  58  31.05 

—0.2489703 

Palermo, 

—  6     1  37.00 

—0.2511227 

Cracow, 

—6  28     2.80 

—0.2694768 

Paramatta, 

—15  12  18.64 

—0.6335491 

Dorpat, 

—6  55     6.02 

—0.2882641 

Paris, 

-  5  17  33.02 

—0.2205211 

Dublin, 

—4  42  50.39 

—0.1964165 

Philadelphia,* 

—  0    7  33.61 

—0.005250.5 

Durham, 

—5     1  52.64 

—0.2096370 

Prague, 

—  6     5  53.52 

—0.2540917 

Edinburgh, 

-4  55  29.34 

—0.2052007 

Pulkowa, 

—  7     9  31.06 

—0.2982757 

Florence, 

—5  53  15.12 

—0.2453139 

Rome, 

—  5  58     8.53 

—0.2487098 

Geneva, 

—5  32  49.24 

—0.2311344 

San  Fernando, 

-  4  43  22.42 

—  0.  1967873 

Georgetown,* 

+0    0     6.20 

+0.0000718 

Santiago, 

—  0  25  30.00 

—0.0177083 

Gottingen, 

—5  47  58.49 

—  0.241G492 

Senftenberg, 

—  6  14     3.00 

—0.2597570 

Gotha, 

—5  51     3.39 

—0.2437892 

Spcyer, 

—  5  41  58.00 

—0.2374769 

Greenwich, 

—5     8  12.39 

—0.2140323 

Stockholm, 

—  6  20  2!i.::r> 

—0.2641939 

Hamburg, 

—5  48    5.95 

—0.2417355 

St.  Petersburg, 

—  7     9  25.87 

—0.2982161 

Hclsingfors, 

—6  48     1.32 

—0.2833486 

Sydney, 

—15  13  12.77 

—  0.63-11758 

Hudson,* 

+0  17  32.06 

+0.0121766 

Upsala, 

-  6  18  42.70 

—0.2629942 

Kasan, 

—8  24  41.14 

—0.3504761 

Utrecht, 

—  5  28  43.67 

—0.2282832 

Konigsberg, 

—0  30  11.87 

—0.2709707 

Vienna, 

—  6  13  44.09 

—0.2595381 

Krcmsmunstcr, 

—6     4  45.03 

—0.2532990 

Wilna, 

—  6  49  23.33 

—0.2842978 

NIITK.—  Tlicsc  Longitudes,  except  of  pi;,,.,.*  ,,,;,,-kr<l  u.ll,  ;1  *,  ;,,-,•  dependent  on  lliat  ofCamhridge,  Mass.,  the  late-t  correc- 
tion of  which  is  -+-  0-'..|<>  =  O'l  .0000053. 

TABLE  II. 


3 


Ninnbrr  tif  Days  i-liijixnl  xiiirr  Ike  "Beginning  <  if  tin-  .1  ill  inn  I'ir/nil,  at  the  Dnli:  .Tun.  0  in  Common  Years, 

tntil  .Inn.  1  IH  liixacjlilr  Yi'iirx. 

vi:  \i:  i\ 

\  i:  AH  iv 

Date  IE 

1  >:iy». 

V.ar. 

U:tt'-  i: 
Solar 

Tin;  CI:N  i  ri:v. 

plx",  : 
(  Ylirrmiiill 

TIII:  <'!•:.  vi  rnv. 

DMVS  from 
previous  (  Yn 
trmiiul  Date. 

I  f  N  . 

It"  I'oMtive. 

Data 

ir  N,  L'.iti>.- 

If  Positive 

—  4718B. 

0 

—  1000 

1356173 

100 

1 

0 

50 

51 

18262 

-1712 

.-{(15   -  !)()() 

1392698 

99 

2 

865 

49B. 

52  B. 

18628 

^1711 

730   -  sOO 

1  129223 

98 

3 

730 

48 

53 

18993 

-4710 

1095 

—  700 

14657  IS 

97B. 

4B. 

1096 

47 

54 

19358 

—  4709B. 

1461 

-  600 

1502273 

96 

5 

1461 

46 

55 

19723 

—  470S 

1826 

—  500 

1538798 

95 

6 

1826 

45B. 

56  B. 

20089 

—4707 

2191 

—  400 

157  5323 

ill 

7 

2191 

44 

57 

20454 

—470(1 

2556 

—  300 

1611848 

93  B. 

8B. 

2557 

43 

58 

20819 

—  4705  B. 

2922 

—  200 

1648378 

92 

9 

2922 

42 

59 

21184 

—  4701 

8287 

—  100 

1684898 

91 

10 

8287 

41  B. 

GOB. 

21550 

—4703 

8652 

1 

1721123 

90 

11 

3652 

40 

61 

21915 

-  1702 

4017 

101 

1757!)  is 

89  B. 

12  B. 

4018 

39 

62 

22280 

—  1701B. 

4383 

201 

171)1173 

88 

13 

4383 

38 

63 

22645 

—4700 

4748 

301 

1830998 

87 

14 

4748 

37B. 

64B. 

23011 

—4600 

41273 

401 

1867523 

86 

15 

5113 

36 

65 

23376 

—  1500 

777!>s 

501 

1904048 

85.B. 

16B. 

5479 

35 

66 

23741 

—  1100 

1  1  13-23 

601 

1910573 

84 

17 

5844 

34 

67 

24106 

—4300 

150s  IS 

701 

1977098 

83 

18 

6209 

33  B. 

68B. 

24472 

—  1-200 

187373 

801 

2013623 

82 

19 

6574 

32 

69 

24837 

—  1100 

•223898 

901 

2050148 

81  B. 

20/J. 

6910 

31 

70 

25202 

—  1000 

260423 

1001 

2086673 

80 

21 

7305 

30 

71 

25567 

—8900 

296!)  IS 

1101    2123198 

79 

22 

7670 

29  B. 

72J5. 

25933 

—3800 

883473 

1201 

2159723 

78 

23 

8035 

28 

73 

26298 

—3700 

869998 

1301 

2  1962  IS 

77  B. 

24B. 

8401 

27 

74 

26663 

—3600 

406523 

1401 

2232773 

76 

25 

8766 

26 

75 

27028 

—3500 

1  13048 

1501 

2269298 

75 

26 

9131 

25  B. 

76B. 

27394 

—3400 

179573 

1583 

2299238 

74 

27 

9496 

24 

71 

27759 

—3300 

516098 

1584B.  2299604 

73B. 

28  B. 

9862 

23 

78 

28124 

—3200 

552628 

1585 

2299969 

72 

29 

10227 

22 

79 

28489 

—3100 

589148 

1586 

2300334 

71 

30 

10592 

2  IB. 

SOB. 

28855 

.  —3000 

625673 

1587 

2300699 

70 

31 

10957 

20 

81 

29220 

—2900 

662198 

15885.  2301065 

69B. 

32  B. 

11323 

19 

82 

29585 

—2800 

698723 

1589 

2301430 

68 

33 

11688 

18 

83 

29950 

—2700 

7352  IS 

1590 

2301795 

67 

31 

12053 

17jB. 

84B. 

30316 

—2600 

771773 

1591 

2302160 

66 

35 

12418 

16 

85 

30681 

—2500 

808298 

1592/J.   2302526 

65B. 

36  B. 

12784 

15 

86 

31046 

—2100 

S  1  1823 

1593 

2302891 

61 

37 

13149 

14 

87 

31411 

—2300 

8813  IS 

1594 

230325(5 

63 

38 

13511 

13B. 

88B. 

31777 

—2200 

917873 

1595 

2303621 

62 

39 

13879 

12 

89 

32142 

—2100 

954398 

1596/J. 

2303987 

61B. 

40B. 

11215 

11 

90 

32507 

—2000 

990923 

1597 

2301352 

60 

41 

14610 

10 

*  91 

32872 

—  1900 

1027  lis 

1598 

2301717 

59 

42 

14975 

9B. 

92  B. 

33238 

—1800 

1063973 

1599 

2305082 

58 

43 

15310 

8 

93 

33603 

—1700 

1  100  498 

1600B.  2305448 

57B. 

44B. 

15706 

7 

94 

33968 

—1600 

1137023 

1601 

2305813 

56 

45 

16071 

6 

95 

34333 

—1500 

11735  IS 

1701 

'23  12337 

55 

46 

16436 

5B. 

96B. 

34699 

—1100 

1210073 

1801    2378861 

51 

47 

16801 

4 

97 

35064 

—1300 

1246598 

1901    2415385 

58£, 

48B. 

17167 

3 

98 

35429 

—  1-200 

1283123    2001 

•2151910 

52 

49 

17532 

2 

99 

35794 

—1100 

1319648 

2101 

51 

50 

17897 

IB. 

100B.  !  36160 

—1000 

1  356  173 

2201 

2524958 

50 

51 

18262 

100 

36159 

I 

G  V 

TABLE  III. 


1 

Number  of  Days  from  Jan.  0  in  Common  Years,  and  Jan.  1  in  Bissextile  Years. 

jANfAi:v.  IT:I;UCAKY. 

! 

1583. 

^ 

;r 

t 

^ 

| 

pi 

a 

gj 

K 

« 

« 

c 

IN 

-, 

£ 

« 

^' 

H 

ca 

a 

A 

M 

H 

a 

s 

§ 

I 

*c 

o 

y. 

i 

H 

u 

" 

A 

t  • 

K 

b 

'J2 
P 

H 

o 

N 

S 

» 

§ 

£ 

£ 

'? 

X 

'- 

p 

o 

E 

O 

B 

«5 

3 

p^ 

<j 

^j 

t? 

- 

r^ 

O 

Pd 

o 

H 

n 

0 

3 

S 

H 

H 

* 

a 

^ 

*» 

66 

° 

fe 

8 

1 

1 

0 

32 

31 

60 

91 

121 

152 

182 

213 

244 

274 

305 

335 

274 

295 

325 

5 

t) 

4i 

1 

33 

32 

61 

92 

122 

153 

183 

214 

245 

275 

30(> 

336 

275 

296 

326 

« 

c 

2 

34 

33 

62 

92 

123 

154 

184 

215 

246 

276 

307 

337 

276 

297 

327 

1 

4 

3 

35 

34 

63 

94 

124 

155 

185 

216 

247 

277 

308 

338 

277 

298 

328 

r 

R 

4 

36 

35 

64 

95  125 

15C 

186 

217 

248 

278 

309 

339 

299 

329 

! 

6 

6 

5 

37 

36 

65 

96 

126 

157 

187 

218 

249 

279 

310 

340 

300 

330 

7 

7 

(1 

38 

37 

66 

97 

127 

158 

188 

219 

250 

280 

311 

341 

301 

334 

8 

N 

7 

39 

38 

67 

98 

128 

159 

189 

220 

251 

281 

312 

312 

302 

332 

9 

9 

8 

40 

39 

68 

99 

129 

160 

190 

221 

252 

282 

313 

343 

303 

333 

10 

10 

9 

41 

40 

69 

100 

130 

161 

191 

222 

253 

283 

314 

344 

304 

334 

11 

11 

10 

42 

41 

70 

101 

131 

162 

192 

223 

254 

284 

315 

345 

305 

335 

12 

12 

11 

43 

42 

71 

102 

132 

163 

193 

224 

255 

285 

316 

346 

306 

336 

13 

13 

12 

44 

43 

72 

103 

133 

164 

194 

225 

256 

286 

317 

317 

307 

337 

11 

14 

13 

45 

44 

73 

104 

134 

165 

195 

226 

257 

287  318 

348 

308 

338 

15 

15 

14 

46 

45 

74 

105 

135 

166 

196 

227 

258 

288 

319 

349 

278 

309 

339 

16 

16 

15 

47 

46 

75 

106 

136 

167 

197 

228 

259 

289 

320 

350 

279 

310 

340 

17 

17 

16 

48 

47 

76 

107 

137 

168  198 

229 

260 

290 

321 

351 

280 

311 

341 

18 

18 

17 

49 

48 

77 

108 

138 

169 

199 

230 

261 

291 

322 

352 

281 

312 

342 

19 

19 

18 

50 

49 

78 

109 

139 

170 

200 

231 

262 

292 

323 

353 

282 

313 

343 

20 

20 

19 

51 

50 

79 

110 

140 

171 

201 

232 

263 

293 

324 

354 

283 

314 

344 

21 

21 

20 

52 

51 

80 

111 

141 

172 

202 

233 

264 

294 

325 

355 

284 

315 

345 

22 

22 

21 

53 

52 

81 

112 

142 

173 

203 

234 

265 

295 

326 

356 

285 

316 

346 

23 

23 

22 

54 

53 

82 

113 

143 

174 

204 

235 

266 

296 

327 

357 

286 

317 

347 

24 

24 

23 

55 

54 

83 

114 

144 

175 

205 

236 

267 

297 

328 

358 

287 

318 

348 

25 

25 

24 

56 

55 

84 

115 

145 

176 

206 

237 

268 

298 

329 

359 

288 

319 

349 

26 
27 
28 
29 

30 

26 
27 
28 
29 
80 

25 

26 
27 

28 
29 

57 
58 
59 

56 
57 
58 
59 

85 
86 
87 
88 
89 

116 
117 
118 
119 
120 

146 
147 
148 
149 
150 

177 
178 
179 
180 
181 

207 
208 
209 
210 
211 

238 
239 
240 
241 
242 

269 
270 
271 
272 
273 

299 
300 
301 
302 
303 

330 
331 
332 
333 
334 

360 
361 
362 
363 
364 

289 
290 
291 
292 
293 

320 
321 
322 
323 
324 

350 
351 
352 
353 
354 

31 

31 

30 

90 

151 

212 

243 

304 

365 

294 

355 

1 

TABLE  IV. 


r> 


/,'  i!  ill-linn  nf  lluiirx.   Miiiu/i-x,  <nul  Scrnmls  nf  Tinir  In   J>i'i'iiiu//.t  nf  u   ])ni/. 

Prrimal  ol'a 
Pay. 

Min. 

Pecimal   ofa 

Pay. 

If  in. 

Drrilllill  lifa 
Pay. 

Decimal  of  a 

See. 

Pi-riina!  ol'a 

Day. 

1 

0.0116667 

1 

0.000(1!)  11 

31          0.0215278 

1 

0.0000116 

31 

o.oQpas 

2 

0.0833333 

2 

0.0013889 

32          0.0222222 

2 

0.0000231 

32 

0.000370  1 

:{ 

0.1250000 

:{ 

0.0020S33 

33          0.022!)  167 

3 

0.0000347 

33 

0.000381!) 

4 

0.166 

;i(i67 

i 

0.0027778 

31          0.0236111 

1 

0.0000  163 

31 

0.00039:!.-) 

5 

0.20N3333 

5 

0.003  1722 

35         0.0243056 

5 

0.0000579 

35 

0.0001051 

6 

0.2500000 

6 

0.0011667 

36          0.0250000 

6 

0.000069  1 

36 

0.0004167 

7 

0.21U6667 

7 

0.0018611 

37          0.02569  1  I 

7 

0.0000810 

37 

0.000  12S2 

8 

0.3333333 

8 

0.0055556 

38         0.0263889 

8 

0.0000926 

:is 

0.000  i:i: 

B 

0.375 

0000 

9 

0.0062500 

39          0.0270833 

9  v 

0.0001012 

39 

0.000151  1 

10 

0.110 

6667 

10 

0.00694  1  1 

40         0.0277778 

10 

0.0001157 

40 

0.0001630 

11 

0.  15S3333 

11 

0.0076389 

41 

0.028  1722 

11 

0.0001273 

41 

0.0004715 

12 

0.5000000 

12 

0.0083333 

12 

0.0291667 

12 

0.0001389 

12 

0.000  iMil 

13 

0.5116667 

13 

0.0090278 

43 

0.0298611 

13 

0.0001505 

13 

0.0004977 

14 

0.5833333 

11 

0.0097222 

44 

0.0305556 

14 

0.0001620 

11 

0.0005093 

rs 

0.6250000 

15 

0.0104167 

45 

0.0312500 

15 

0.0001736 

45 

0.0005208 

16 

0.6666667 

16 

0.0111111 

46 

0.0319414 

16 

0.0001852 

46 

0.0005324 

17 

0.70S3333 

17 

0.0118056 

47 

0.0326389 

17 

0.0001968 

47 

0.0005110 

18 

0.7500000 

18 

0.0125000 

48 

0.0333333 

18 

0.0002083 

48 

0.0005556 

19 

0.7916667 

1!) 

0.0131!)  11 

49    .      0.0340278 

19 

0.0002199 

49 

O.ooo:.!i7  1 

20 

O.S333333 

20 

0.0138889 

50 

0.0317222 

20 

0.0002315 

50 

0.0005787 

21 

O.S750000 

21 

0.0115833 

51 

0.0354167 

21 

0.0002431 

51 

0.0005903 

22 

0.9  If 

6667 

22 

0.0152778 

52 

0.0361111 

22 

0.0002546 

52 

0.0006019 

23 

0.95N3333 

23 

0.0159722 

53 

0.0368056 

23 

0.0002662 

53 

0.00061:!! 

21 

1.0000000 

24 

0.0166667 

51 

0.0375000 

24 

0.0002778 

51 

0.0006250 

25 

0.0173611 

55 

0.0381944 

25 

0.0002894 

55 

0.0006366 

26 

0.0180556 

56 

0.0388889 

26 

0.0003009 

56 

0.0006481 

27 

0.0187500 

57 

0.0395833 

27 

0.0003125 

57 

0.0006597 

28 

0.0191111 

58 

0.0402778 

28 

0.0003241 

58 

0.0006713 

29 

0.0201389 

59 

0.0409722 

29 

0.0003356 

59 

0.0006829 

30 

0.0208333 

60 

0.0416667 

30 

0.0003472 

60 

0.00069  1  I 

TABLE   V. 

Periods  of  the  Arguments  with  their  multiples. 

Increments  of  Arguments 

X-XIVfnr  an  incri'tiai- 

of  1,2  and  3  in  the  integer  ill. 

1   Period. 

2  Periods. 

3  Periods. 

Argument  I 

22  1''.7008 

419'UOH! 

674d.1023 

Increment 

Increment        Increment 

II 

23S\9 

477-v.S 

716J-.8 

/.          ..            f  ,„       .1 

01  nl  ==  *i            ol  HI  ^=  d. 

III 

11967*. 

23974d. 

35962'1. 

IV 

2969*. 

5918*. 

8878d. 

V 

1454d.9 

2909-'.9 

4364d.8 

Argument  X 

33.26 

6.52             39.78 

VI 

583''.92 

1167".84 

175  K76 

XI 

"       XII 

147.64 
19.6 

55.29          202.93 
39.3               58.9 

«        VII 

213''.16 

486''.33 

729''.49 

"      XIII 

3.11 

6.22               9.34 

"      VIII 

220''.6 

440'».1 

661*.7 

"     XIV 

0.8 

1.5                2.3 

IX 

236'1.99 

473''.98 

710".98 

X 

60  units 

120  units 

180  units 

- 

XI 

240  units 

480  units 

720  units 

»       XII 

60  units 

120  units 

!•>()  units 

«      XIII 

60  units 

120  units 

180  units 

"      XIV 

36  units 

72  units 

108  units 

«      \v 

8796*3 

13596''.5 

2039  l-'.M 

»      XVI 

365''.2 

730''.5 

1095''.7 

TABLE  VI. 


Mean  Longitude,  Arguments,  tyc.,  for  Wa^hin^lon  Mean  Noon  of  Jan.  0  in  common  years,  Jan.  1  in 
bissextile,  years. 

\ 

Year. 

L 

in- 

I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

1750 

o   /    // 

45  54  5.24 

-163 

173.9096 

67:9 

d 

1  12  42 

2403 

d 

611.5 

497.08 

31.2 

1751 

270  41  31.89     161 

89.5080 

68.9 

11607 

2768 

976.5 

278.16 

153.0 

17525. 

137  5  12.35     159 

6.1064 

69.9 

11973 

175 

1342.5 

60.24 

32.7 

1753 

1  52  42.00 

158 

146.4056 

70.9 

351 

540 

252.5 

425.24 

154.5 

1754 

226  40  11.66 

156 

62.0040 

71.9 

716 

905 

617.5 

206.32 

33.2 

1755 

91  27  41.31 

—155 

202.3032 

72.9 

1081 

1270 

982.5 

571.32 

155.0 

175GB. 

317  51  18.77 

153 

118.9016 

73.9 

1447 

1636 

1348.5 

353.40 

34.7 

1757 

182  38  48.42 

151 

34.5000 

74.9 

1812 

2001 

258.6 

134.48 

156.5 

1758 

47  26  18.08 

150 

174.7993 

75.9 

2177 

2366 

623.6 

499.48 

35.2 

1759 

272  13  47.73 

148 

90.3977 

76.9 

2542 

2731 

988.6 

280.56 

157.1 

17(507?. 

138  37  25.19 

—146 

6.9961 

77.9 

2908 

137 

1354.6 

62.63 

36.7 

1761 

3  24  54.84 

145 

147.2953 

78.9 

3273 

502 

264.7 

427.63 

158.6 

1702 

228  12  24.50 

143 

62.8937 

79.9 

3638 

867 

629.7 

208.71 

37.2 

1763 

92  59  51.15 

142 

203.1929 

80.9 

4003 

1232 

994.7 

573.71 

15^.1 

17645. 

319  23  31.61 

140 

119.7913 

81.9 

4369 

1598 

1360.7 

355.79 

38.7 

1765 

184  11  1.27 

—138 

35.3898 

82.9 

4734 

1963 

270.7 

136.87 

160.6 

1766 

48  58  30.92 

137 

175.6890 

83.9 

5099 

2328 

635.7 

501.87 

39.2 

1767 

273  46  0.58 

135 

91.2874 

84.9 

5464 

2693 

•1000.7 

282.95 

161.1 

17685. 

140  9  38.04 

133 

7.8858 

85.9 

5830 

100 

1366.7 

65.03 

40.7 

1769 

4  57  7.69 

132 

148.1850 

86.9 

6195 

465 

276.8 

430.03 

162.6 

1770 

229  44  37.35 

—130 

63.7834 

87.9 

6560 

830 

641.8 

211.11 

41.3 

1771 

94  32  7.00 

129 

204,0826 

88.9 

6925 

1195 

1006.8 

576.11 

163.1 

17725. 

320  55  44.47 

127 

120.6811 

89.9 

7291 

1561 

1372.8 

358.18 

42.8 

1773 

185  43  14.12 

125 

36.2795 

90.9 

7656 

1926 

282.9 

139.26 

164.6 

1774 

50  30  43.78 

124 

176.5787 

91.9 

8021 

2291 

647.9 

504.26 

43.3 

1775 

275  18  13.43 

—  122 

92.1771 

92.9 

8386 

2656 

1012.9 

285.34 

165.1 

1776B. 

141  41  50.89 

120 

8.7755 

93.9 

8752 

63 

1378.9 

67.42 

44.8 

1777 

6  29  20.55 

119 

149.0748 

94.9 

9117 

428 

288.9 

432.42 

166.6 

1778 

231  16  50.21 

117 

64.6732 

95.9 

9482 

793 

653.9 

213.50 

45.3 

1779 

96  4  19.86 

116 

204.9724 

96.9 

9847 

1158 

1018.9 

578.50 

167.1 

17801?. 

322  27  57.32 

—  114 

121.5708 

97.9 

10213 

1524 

1384.9 

360.58 

46.8 

1781 

187  15  26.98 

112 

37.1692 

98.9 

10578 

1889 

295.0 

141.66 

168.6 

1782 

52  2  56.64 

111 

177.4684 

99.9 

10943 

2254 

660.0 

506.66 

47.3 

1783 

276  50  26.29 

109 

93.0669 

100.9 

11308 

2619 

1025.0 

287.74 

169.1 

17845. 

143  14  3.76 

107 

9.6653 

101.9 

11674 

26 

1391.0 

69.81 

48.8 

1785 

8  1  33.41 

—106 

149.9645 

102.9 

52 

391 

301.0 

434.81 

170.6 

1786 

232  49  3.07 

104 

65.5629 

103.9 

417 

756 

666.0 

215.89 

49.3 

1787 

97  36  32.73 

103 

205.8621 

104.9 

782 

1121 

1031.0 

580.89 

171.1 

17885. 

324  0  10.19 

101 

122.4605 

105.9 

1148 

1487 

1397.0 

362.97 

50.8 

1789 

188  47  39.85 

99 

38.0590 

106.9 

1513 

1852 

307.1 

144.05 

172.6 

1790 

53  35  9.51 

—  98 

178.3582 

107.9 

1878 

2217 

672.1 

509.05 

51.3 

1791 

278  22  39.16 

96 

93.9566 

108.9 

2243 

2582 

1037.1 

290.13 

173.1 

17927?. 

144  46  16.63 

94 

10.5551 

109.9 

2609 

2948 

'  1403.1 

72.21 

52.8 

1793 

9  33  46.28 

93 

150.8543 

110.9 

2974 

354 

313.2 

437.21 

174.6 

1794 

234  21  15.94 

91 

66.4527 

111.9 

3339 

719 

678.2 

218.29 

53.3 

1795 

99  8  45.60 

—  90 

206.7519 

112.9 

3704 

1084 

1043.2 

583.29 

175.2 

17965. 

325  32  23.07 

88 

123.3503 

113.9 

4070 

1450 

1409.2 

365.36 

54.8 

1797 

190  19  52.72" 

86 

88.9488 

114.9 

4435 

•  1815 

319.2 

146.44 

176.7 

1798 

55  7  22.38 

85 

179.2480 

115.9 

4800 

2180 

684.2 

511.44 

55.3 

1799 

279  54  52.04 

—  83 

94.8464 

116.9 

5165 

2545 

1049.2 

292.52 

177.2 

Constant  subtracted  from  L  =  47'  4li". 


TABL.E    VI. 


Minn  Ltnin'iliidf,  Arguments,  cV''.,  /<>/'   M'n.-i/iiinffiiti  Menu  J\"<HI;I  »J    Jim.  0  in  romuinn  yrtirs.  Jim.   I  in 
l>ixxi'.ili/i-  i/i-firx. 

Fear. 

VIII. 

IX. 

X. 

M. 

XII. 

Xlil. 

XIV. 

Log.  sin  i. 

:wo°-  Q. 

1760 

a 
55.9 

2858 

43.96 

193.  IS 

4N.7 

58.45 

22.7 

S.77207SS 

0          /               // 

2s.)  31    16.8 

I?.')  1 

200.3 

156.29 

50.  IS 

8.71 

28.0 

4.67 

2  1.2 

0802 

33    1  1.3 

1752JB. 

125.2 

56.99 

64.06 

7.2 

10.89 

25.7 

OS  15 

33   11.8 

1753 

49.1 

176.31 

30.25 

211.70 

26.9 

14.01 

26.6 

0829 

32  39.3 

1754 

193.5 

67.33 

86.77 

26.99 

6.1 

20.23 

28.0 

OS  12 

32     6.9 

1755 

117.1 

195.31 

10.03 

17  1.63 

25.7 

23.3  I 

28.7 

N.7720856 

285  31  31,1 

ii  MI:. 

42.2 

87.85 

16.55 

229.  92 

5.0 

29.5!! 

30.2 

OS70 

31      l.s 

1757 

186.7 

215.36 

23.06 

15.21 

44,2 

35.79 

31.7 

0883 

30  29,1 

1758 

110.5 

10(i.3S 

56.33 

192.  Mi 

8.9 

38.90 

32.5 

0897 

2!)  5li.9 

1759 

34.4 

231.3S 

•2.S  1 

8.15 

43.  1 

45.12 

34.0 

0911 

29  21.1 

1760B. 

179.8 

12(5.10 

9.36 

63.  1  1 

22.  1 

51.35 

35.5 

8.7720924 

285  28  51.9 

1761 

103.7 

17.12 

42.62 

211.08 

12.0 

54.46 

0.2 

0938 

2S   19.1 

1763 

27.6 

1  15.  13 

49.13 

26.37 

21.2 

0.68 

1.7 

0951 

27  47.0 

1763 

172.0 

3(i.  1  1 

22.39 

n  1.02 

40.9 

3.79 

2.5 

0965 

27  14.5 

1764B. 

9G.9 

165.45 

28.91 

229.31 

20.1 

10.02 

4.0 

0979 

26  41.9 

1765 

•20.7 

56.47 

35,13 

44.60 

59.4 

16.24 

5.5 

8.7720992 

285  26     9.5 

1766 

1655 

IS  1.17 

8.68 

192.2  1 

19.0 

19.35 

6.2 

1006 

25  37.0 

1767 

89.0 

75.  lit 

15.20 

7.5:! 

5S.2 

25.58 

7.7 

1020 

25    4.5 

17685. 

13.9 

201.50 

21.72 

62.82 

37.5 

31.80 

9.2 

1033 

24  32.0 

1769 

ir>s.  i 

95.51 

51.98 

210,16 

57.1 

34.91 

10.0 

1047 

23  59.5 

1770 

82.2 

823.53 

1.49 

25.75 

36,1 

41.14 

11.5 

8.7721060 

285  23  27.0 

1771 

6.1 

1  1  1.5  1 

8475 

173.40 

56.0 

44.25 

12.3 

1071 

22  51.6 

1772B. 

151.5 

6.55 

41.27 

228.69 

35.2 

50.47 

13.8 

loss 

22  22.0 

1773 

7.'..  1 

134.56 

47.7!) 

48.98 

14.5 

56.69 

15.3 

1101 

21  49.5 

1771 

•219.8 

85.58 

21.05 

191.62 

31.1 

59.81 

16.0 

1115 

21   17.1 

1775 

1  13.7 

153.59 

27.5(5 

6.91 

13.4 

6.03 

17.5 

8.7721128 

285  20  44.6 

1776J5. 

68.6 

45.60 

31.08 

62.20 

52.6 

12.25 

19.0 

1142 

20  12.1 

1777     . 

213.0 

173.61 

7.31 

209.85 

12.2 

15.37 

19.8 

1156 

19  39.6 

1778 

136.9 

64.63 

13.86 

25.14 

51.5 

21.59 

21.3 

1169 

19     7.1 

1779 

60.7 

192.64 

47.12 

172.78 

11.1 

24.70 

22.0 

1183 

18  31.6 

1780.B. 

206.2 

84.65 

53.63 

228.07 

50.4 

30.92 

23.5 

8.7721197 

285  18    2.1 

1781 

130.0 

212.66 

0.15 

43.?6 

29.6 

37.15 

25.0 

1210 

17  29.6 

178-2 

53.9 

103.68 

33.11 

191.00 

49.2 

40.26 

25.8 

1224 

16  57.1 

1783 

198.3 

231.68 

39.93 

6.29 

28.5 

46.48 

27.3 

1237 

16  24.7 

17845. 

123.2 

123.70 

46.44 

61.58 

7.7 

52.71 

28.8 

1251 

15  52.1 

1785 

47.1 

1  1.72 

19.70 

209.23 

27.4 

55.82 

29.5 

8.7721265 

285  15  19.6 

1786 

191.5 

142.72 

26.22 

21.52 

6.6 

2.04 

31.1 

127S 

14  47.1 

1787 

115.1 

33.7  1 

59.48 

172.16 

26.2 

5.15 

31.8 

1292 

14  14.7 

17885. 

40.2 

102.75 

6.00 

227.45 

5.5 

11.38 

33.3 

1306 

13  42.1 

1789 

184.7 

53.76 

12.51 

42.74 

41.7 

17.60 

34.8 

1319 

13     9.6 

1700 

108.5 

181.77 

15.77 

190.39 

4.4 

20.71 

35.6 

8.7721333 

285  12  37.2 

1791 

32.4 

72.71) 

52.29 

5.68 

43.6 

26.94 

1.1 

1346 

12    4.7 

17925. 

177.8 

201.80 

58.81 

60.97 

22.9 

33.16 

2.6 

1360 

11  32.1 

17!):! 

101.7 

92.81 

32.06 

208.61 

42.5 

36.27 

3.3 

1374 

10  59.7 

1794 

25.6 

220.82 

38.58 

23.90 

21.7 

42.50 

4.8 

1387 

10  27.2 

1795 

170.0 

111.84 

11.84 

171.51 

11.1 

15.61 

5.6 

8.7721401 

285    9  51.7 

17965. 

91.9 

3.85 

18.36 

226.83 

20.6 

51.83 

7.1 

-    1415 

9  22.1 

1797 

18.7 

131.86 

24.87 

12.12 

59.9 

58.05 

8.6 

112S 

8  49.7 

1798 

163.2 

22.88 

58.13 

189.77 

19.5 

1.17 

9.3 

1442 

8  17.2 

1799 

87.0 

150.89 

4.65 

5.06 

58.7 

7.39 

10.8 

8.7721456 

285     7  41.7 

TABLE    VI. 


3[ca»  Luiii/i/iiili',  Ariinmnitx,  <fr.,  fur  Wellington  j\Imn  Xo<>n  of  Jnn.  o  in  cvtomm  years,  .run.  1  in 
lii.-inr.i-lilc  unit's. 

Year. 

L. 

HI- 

I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

1800 

0      /      // 

144  42  21.70 

—81 

10,1118 

117!9 

553o' 

29  lo" 

llli!2 

73JGO 

<i 
55.8 

1801 

9  29  51.36 

80 

150.7111 

118.9 

5895 

315 

324.3 

438.60 

177.7 

1802 

234  17  21.02 

78 

66.3125 

119.9 

6260 

680 

689.3 

219.68 

56.3 

1803 

99  4  50.67 

77 

206.6417 

120.9 

6625 

1015 

1054.3 

0.76 

178.2 

18042?. 

325  28  28.14 

75 

123.2401 

121.9 

6991 

1411 

1420.3 

366.76 

57.8 

1805 

100  15  57.80 

—73 

38.8386 

122.9 

735G 

1776 

330.4 

1  17.84 

179.7 

1808 

55  3  27,16 

72 

179.1378 

123.9 

7721 

2111 

695.4 

512.84 

58.3 

1807 

279  50  57.12 

70 

94.7362 

121.9 

8086 

2508 

1060.4 

293.91 

180.2 

1808B. 

116  11  31.58 

68 

11.  33  16 

125.9 

8452 

2872 

1426.4 

75.99 

59.9 

1809 

1  1  2  4.24 

67 

151.6339 

126.9 

8817 

278 

336.4 

110.99 

181.7 

1810 

235  49  33.90 

—65 

67.2323 

127.9 

9182 

613 

701.4 

222.07 

60.4 

1811 

100  37  3.56 

64 

207.5315 

128.9 

9517 

1008 

1066.4 

3.15 

182.2 

18127?. 

327  0  41.03 

62 

121.1299 

129.9 

9913 

1374 

1432,1 

369.15 

61.9 

1813 

191  48  10.69 

60 

39.7284 

130.9 

10278 

1739 

342.5 

150.23 

183.7 

1814 

56  35  40.35 

59 

180.0276 

131.9 

10643 

2104 

707.5 

515.23 

62.4 

1815 

281  23  10.01 

—57 

95.6260 

132.9 

11008 

2469 

1072.5 

296.31 

184.2 

1816B. 

147  46  47.47 

55 

12.2245 

133.9 

11374 

2835 

1438.5 

78.39 

63.9 

1817 

12  34  17.13 

54 

152.5237 

134.9 

11739 

241 

348.6 

443.39 

185.7 

1818 

237  21  46.79 

52 

68.1221 

135.9 

116 

606 

713.6 

224.46 

64.4 

1819 

102  9  16.45 

51 

208.4213 

136.9 

481 

971 

1078.6 

5.54 

186.2 

18207?. 

328  32  53.92 

—49 

125.0198 

137.9 

817 

1337 

1444.6 

371.54 

65.9 

1821 

193  20  23.58 

47 

40.6182 

138.9 

1212 

1702 

35  1.6 

152.62 

187.7 

1822 

53  7  53.24 

46 

180.9174 

139.9 

1577 

2067 

719.6 

517.62 

66.4 

1823 

282  55  22.90 

44 

96.5159 

140.9 

1942 

2432 

1084.6 

298.70 

188.2 

18217?. 

149  19  0.37 

42 

13.1143 

141.9 

2308 

2798 

1450.6 

80.78 

67.9 

18-25 

14  6  30.03 

—41 

153,1135 

142.9 

2673 

204 

360.7 

445.78 

189.7 

1826 

238  53  59.69 

39 

69.0119 

143.9 

3038 

569 

725.7 

226.86 

68.4 

1827 

103  41  29.36 

38 

209.3112 

144.9 

3103 

934 

1090.7 

7.94 

190.2 

18287?. 

330  5  6.82 

36 

125.9096 

145.9 

37G9 

1300 

1.8 

373.94 

69.9 

1829 

194  52  36.49 

31 

41.5080 

146.9 

4134 

1665 

366.8 

155.02 

191.7 

1830 

59  40  6.15 

—33 

181.8073 

147.9 

4499 

2030 

731.8 

520.02 

70.4 

1831 

284  27  35.81 

31 

97.4057 

148.9 

4884 

2395 

1096.8 

301.09 

192.2 

issjiB. 

150  51  13.28 

29 

11.0041 

149.9 

5230 

2761 

7.8 

83.17 

71.9 

1833 

,   15  38  42.94 

28 

151.3034 

150.9 

5595 

167 

372.8 

448.17 

193.8 

1831 

240  26  12.60 

26 

69.9018 

151.9 

5960 

532 

737.8 

229.25 

72.4 

1835 

105  13  42.27 

—25 

210.2010 

152.9 

6325 

897 

1102.8 

10.33 

194.3 

18367?. 

331  37  19.73 

23 

126.7995 

153.9 

6691 

1263 

13.9 

376.33 

73.9 

1837 

196  24  49.40 

21 

42.3979 

154.9 

7056 

1628 

378.9 

157.41 

195.8 

1838 

61  12  19.06 

20 

182.6971 

155.9 

7421 

1993 

713.9 

522.11 

74,4 

1839 

285  59  48.72 

18 

98.2956 

156.9 

7786 

2358 

1108.9 

303.49 

196.3 

18107?. 

152  23  26.19 

—16 

14.8940 

157.9 

8152 

2724 

19.9 

85.57 

75.9 

1811 

17  10  55.86 

15 

155.1932 

158.9 

8517 

129 

384.9 

450.57 

197.8 

1812 

211  58  25.52 

13 

70.7917 

159.9 

8882 

494 

749.9 

231.64    76.4 

1843 

106  45  55.  IN 

12 

211.0909 

160.9 

9247 

859 

1114.9 

12.72 

198.3 

18447?. 

333  9  32.65 

10 

127.6893 

161.9 

9613 

1225 

26.0 

378.72 

77.9 

1845 

197  57  2.32 

—  8 

43.2878 

162.9 

9978 

1590 

391.0 

159.80   199.8 

1846 

62  44  31.98- 

7 

183.5870 

163.9 

10343 

1955 

756.0 

521.80    78.5 

1817 

287  32  1.65 

5 

99.1854 

164.9 

10708 

2320 

1121.0 

305.88   200.3 

IS  is/;. 

153  55  39.12 

3 

15.7839 

165.9 

11074 

2686 

32.1 

87.96    80.0 

181!) 

18  43  8.78 

—  2 

156.0831 

166.9 

11439 

92 

397.1 

452.96 

201.8 

Constant  subtracted   from   L  =  47'  40". 


TABLE   VI. 


i—  • 

M  i-ii  n  I.oiii/ititilt',  Ari/iniioitx.  «tr.,/w  Wasl/hii/lon  Muni  Xoon  of  Jan.  0  in  common  ymrx,  ,Imt.  I  in 
binm-j-tilc  ynti-N. 

VIII. 

IX. 

\. 

XI. 

XII. 

XIII. 

XIV. 

1  „'>;_'.  *'"  '• 

360°  -  Q. 

.1 

1 

0            /           // 

1800 

10.9 

11.90 

11.17 

60.85 

38.0 

13.61 

12.:! 

8.7721469 

285     7   12.2 

1801 

155.3 

169.91 

44.43 

207.99 

57.11 

16.72 

18.1 

UN;! 

6  39.8 

1802 

79.2 

60.98 

50.94 

23.28 

86.9 

22.95 

14.6 

i  !!><; 

6     7.3 

1803 

8.1 

188.93 

2  1.20 

170.93 

56.5 

26.06 

15.4 

1510 

5  31.  s 

IMII/;. 

1  is.;, 

30.72 

226.22 

35.7 

82.3 

16.9 

1523 

5     2.2 

7-.'.  1 

206.96 

87.24 

41.51 

15.0 

3S.51 

18.4 

8.7721537 

285     4  29.8 

1806 

-,'l 

99.98 

10.50 

189.15 

84.6 

41.62 

19.1 

1550 

3  57.3 

1807 

1  10.7 

221 

17.01 

1.11 

13.9 

17.84 

20.6 

1564 

3  21.8 

1808B. 

65.5 

120.00 

2;!..-):( 

59.73 

53.1 

51.07 

22.1 

I  :.',  . 

2  52.2 

1809 

210.0 

11.02 

56.79 

207.37 

12.7 

57.18 

22.9 

1591 

2  19.7 

1810 

183.8 

1:59.02 

8.81 

22.66 

52.0 

3.10 

21.1 

8.7721605 

285     1  47.3 

1811 

57.7 

30.04 

86.! 

170.31 

11.6 

6.51 

25.1 

1618 

1    ll.H 

1812B. 

203.  1 

159.05 

48.08 

225.60 

50.9 

12.71 

26.6 

1632 

0  42.2 

1813 

127.0 

50.06 

49.60 

40.8!) 

30.1 

18.96 

28.1 

1646 

2*5     0     9.7 

1814 

50.9 

i:  <.o? 

22.86 

1S8.53 

49.7 

22.07 

28.9 

1659 

281  59  37.2 

1815 

195.3 

69,09 

29.37 

8.82 

29.0 

28.30 

30.4 

8.7721673 

284  59     4.U 

;  .;/;. 

120.2 

198.10 

35.89 

59.  1  1 

84.52 

31.9 

1686 

58  32.2 

1817 

44.0 

89.11 

9.15 

206.76 

27.9 

87.63 

32.6 

1700 

57  59.7 

217.12 

15.66 

22.05 

7.1 

48.85 

31.1 

1713 

57  -2'i:'. 

1819 

112.3 

108.14 

48.93 

169.69 

26.7 

48.97 

31.9 

1727 

56  51.7 

18302?. 

37.2 

0.15 

55.  1  1 

221.98 

6.0 

58.19 

0.4 

8.7721741 

281  56  22.2 

1821 

181.6 

128.16 

1.96 

10.27 

45.2 

59.11 

1.9 

1751 

55  49.T 

1823 

105.5 

19.18 

35.22 

187.91 

4.9 

2.53 

2.7 

1768 

55  17.2 

1823 

•J!>.  1 

117.19 

11.71 

3.20 

44.1 

8.75 

4.2 

1781 

54  44.7 

1824B. 

174.8 

39.20 

4H.25 

58.49 

23.  1 

14.97 

5.7 

1795 

51   12.2 

1829 

98.7 

167.21 

21.51 

206.14 

43.0 

18.08 

6.4 

8.7721808 

284  53  39.7 

1826 

22.6 

58.23 

28.03 

21.43 

22.2 

21.31 

7.9 

1S22 

53     7.2 

1827 

107.0 

186.23 

1.29 

169.07 

41.9 

27.42 

8.7 

1836 

52  34.7 

10289. 

91.9 

78.25 

7.81 

22  1.36 

21.1 

33.64 

10.2 

1849 

52     2.1 

1829 

15.7 

206.26 

14.82 

39.65 

0.4 

39.87 

11.7 

1863 

51  29.6 

1830 

160.2 

97.27 

47.58 

187.30 

20.0 

12.98 

12.1 

8.7721876 

284  50  57.1 

1831 

84.0 

22558 

51.10 

2.59 

59.2 

49.20 

13.9 

1890 

50  24.7 

1882.8. 

8,9 

117.30 

0.62 

57.88 

38.5 

55.43 

15.4 

1901 

49  52.1 

1S33 

153.3 

8.82 

33.88 

205.52 

58.1 

58.54 

16.2 

1917 

49  19.6 

1834 

77.2 

186.32 

40.39 

20.81 

37.4 

4.76 

17.7 

1931 

48  47.1 

1--:;:, 

1.1 

27,84 

13.65 

168.45 

57.0 

7.87 

18.4 

8.7721911 

284  48  11.6 

18865. 

1  16.5 

156.85 

20.17 

223.74 

86.2 

14.10 

19.9 

1958 

47  42.0 

1887 

70.1 

17.86 

26,69 

39.03 

15.5 

20.32 

21.5 

1971 

47     9.6 

1838 

211.S 

175.37 

59.94 

186.68 

35.1 

23.  13 

22.2 

1985 

46  37.1 

1839 

188.7 

66.39 

6.46 

1.97 

14.4 

29.66 

23.7 

1999 

46     1.6 

is  i()/;. 

63.5 

195.40 

12.98 

57.26 

53.6 

35.88 

25.2 

8.7722012 

284  45  32.0 

1841 

208.0 

86.41 

46.24 

20  1.90 

13.2 

38.99 

26.0 

2026 

44  59.5 

1842 

131.8 

21442 

52.75 

20.19 

52.5 

15.21 

27.5 

2039 

44  27.0 

1813 

55.7 

105.44 

26.01 

167.84 

12.1 

18.33 

23.2 

2053 

13  51.5 

1844B. 

201.1 

234.44 

82.53 

223.  13 

51.4 

54.55 

29.7 

2067 

43  21.9 

1845 

12f>.0 

125.  1(5 

39.05 

3S.  12 

30.6 

0.77 

31.2 

8.7722080 

284  42  49.5 

IM  ; 

4K.9 

16.48 

12.31 

186.06 

50.2 

3.88 

32.0 

209  1 

12   17.0 

1847 

193.3 

144.49 

18.82 

1.35 

29.5 

10.11 

33.5 

2107 

11    11.5 

IMS/;.      ii 

86.50 

25.3  1 

56.64 

8.7 

16.33 

35.0 

2121 

41   11.9 

1849 

12.0 

Hi  1.51 

58.60 

201.28 

28.4 

19.  1  1 

35.7 

8.7722131 

284  40  3!).  1 

1 

10 


TABLE  VI. 


Mean  Longitude,  Arguments,  $c.,  for  Washington  Mean  Xoon  of  Jan.  0  in  common  years,  Jan.  I  in 
bissextile  i/ears. 

Year. 

L 

HI- 

I. 

11. 

III. 

IV. 

V. 

VI. 

VII. 

1850 

243°  30  38.45 

0 

71.6815 

167?9 

11804 

a 
457 

d 

702.1 

284.04 

SO'!5 

1851 

108  18  8.11 

1 

211.9808 

168.9 

182 

822 

1127.1 

15.12 

202.3 

1862J9. 

334  41  45.58 

3 

128.5792 

169.9 

548 

1188 

38.1 

381.12 

82.0 

1853 

199  29  15.25 

5 

44.1776 

170.9 

913 

1553 

403.1 

102.19 

202.8 

1851 

64  16  44.92 

6 

184.4769 

171.9 

1278 

1918 

768.1 

527.19 

82.5 

1859 

289  4  11.58 

8 

100.0753 

172.9 

1643 

2283 

1133.1 

308.27 

204.3 

185GB. 

155  27  52.05 

.  10 

16.6738 

173.9 

2009 

2649 

44.2 

90.35 

84.0 

1867 

20  15  21.72 

11 

156.9730 

174.9 

231  I 

55 

409.2 

455.35 

205.8 

1858 

245  2  51.39 

13 

72.5715 

175.9 

2739 

420 

774.2 

236.43 

84.5 

1859 

109  50  21.05 

14 

212.8707 

176.9 

3104 

785 

1139.2 

17.51 

206.3 

18605. 

330  13  58.53 

16 

129.4691 

177.9 

3470 

1151 

50.3 

383.51 

86.0 

1861 

201  1  28.19 

18 

45.0675 

178.9 

3835 

1516 

415.3 

164.59 

207.8 

1864 

65  48  57.86 

19 

185.3668 

179.9 

4200 

1881 

780.3 

529.59 

86.5 

1868 

290  36  27.53 

21 

100.9052 

180.9 

4665 

2210 

1  145.3 

310.67 

208.3 

18645. 

157  0  5.00 

23 

17-5637 

181.9 

4931 

2612 

56.3 

92.75 

88.0 

1865 

21  47  31.67 

24 

157.8629 

182.9 

5296 

18 

421.3 

457.75 

209.8 

1866 

246  35  4.31 

26 

73.4613 

183.9 

5661 

383 

786.3 

238.82 

88.5 

1807 

111  22  31.00 

27 

213.7606 

184.9 

6026 

748 

1151.3 

19.90 

210.3 

18685. 

337  46  11.48 

29 

130.3590 

185.9 

6392 

1114 

62.4 

385.90 

90.0 

1869 

202  33  41.15 

31 

45.9575 

186.9. 

6757 

1479 

427.4 

166.98 

211.8 

1870 

67  21  10.82 

82 

186.2567 

187.9 

7122 

1844 

792.4 

531.98 

90.5 

1871 

292  8  40.49 

31 

101.8551 

188.9 

7487 

2209 

1157.4 

313.06 

212,1 

18725. 

158  32  17.96 

36 

18.4536 

189.9 

7853 

2575 

68.5 

95.14 

92.0 

1873 

23  19  47.63 

37 

158.7528 

190.9 

8218 

2940 

433.5 

460.14 

213.9 

1874 

248  7  17.30 

39 

74.3513 

191.9 

8583 

346 

798.5 

241.22 

92.5 

1875 

112  54  46.97 

40 

214.6505 

192.9 

8948 

711 

1163.5 

22.30 

214.4 

1876  B. 

339  18  24.45 

42 

131.2189 

193.9 

9314 

1077 

71.5 

388.30 

94.0 

1877 

201  5  54.12 

44 

46.8474 

194.9 

9679 

1442 

439.5 

169.37 

215.9 

1878 

68  53  23.79 

45 

187.1466 

195.9 

10044 

1807 

804.5 

534.37 

94.5 

1879 

293  40  53.46 

47 

102.7451 

196.9 

10409 

2172 

1169.5 

315,15 

210,1 

1880  //. 

160  4  30.94 

49 

19.3435 

197.9 

10775 

2538 

80.6 

97.53 

96.0 

1881 

24  52  0.61 

50 

159.6428 

198.9 

11140 

2903 

445.6 

462.53 

217.9 

1882 

249  39  30.28 

53 

75.2412 

199.9 

11505 

308 

810.6 

243.01 

90.6 

1883 

114  26  59.95 

53 

215.5404 

200.9 

11870 

673 

1  175.6 

24.69 

218,4 

18845. 

340  50  37.43 

55 

132.1389 

201.9 

249 

1039 

86.6 

390.69 

98.1 

1885 

205  38  7.10 

57 

47.7373 

202.9 

615 

1404 

451.6 

171.77 

219.9 

1886 

70  25  36.77 

58 

188.0366 

203.9 

980 

1769 

816.6 

536.77 

98.6 

1887 

295  13  6.45 

60 

103.6350 

204.9 

1315 

2134 

1181.6 

317.85 

220.4 

1888  B. 

161  36  43.93 

62 

20.2335 

205.9 

1711 

2500 

92.7 

99.92 

100.1 

1889 

26  24  13.60 

63 

160.5327 

206.9 

2076 

2865 

457.7 

464.92 

221.9 

1890 

251  11  43.27 

65 

76.1312 

207.9 

2111 

271 

822.7 

246.00 

100.6 

1S91 

115  59  12.95 

66 

216.1:!()1 

208.9 

2808 

636 

1187.7 

27.08 

222,1 

18922?. 

342  22  50.43 

68 

133.0289 

209.9 

3172 

1002 

98.8 

393.08 

102.1 

1893 

207  10  20.10 

70 

48.6273 

210.9 

3537 

1367 

463.8 

174.16 

223.9 

1894 

71  57  49.78 

71 

188.9265 

211.9 

3902 

1732 

828.8 

539.16 

102.6 

1895 

296  45  19.45 

73 

101.5250 

212.9 

4267 

2097 

1193.8 

320.24 

224.4 

18965. 

163  8  56.!)3 

75 

21.12:55 

213.9 

4033 

2463 

104.8 

102.32 

104.1 

1897 

27  50  26.61 

76 

161.4227 

214.9 

4998 

2828 

409.8 

467.32 

225.9 

1898 

252  43  56.29 

78 

77.0211 

215.9 

5303 

234 

834.8 

248.40 

104.6 

1899 

117  31  25.96 

79 

217.3201 

216.9 

5728 

599 

1199.8 

29,18 

226.4 

Constant  subtracted   from   L  =  •!?'  -10". 


TABLE    VI. 


11 


M'  dit  Lunijitiiilr,  Ar^uinnilx,  <$-r.,  fur  Wiixlihiatoti  Mruii  Xnon  of  Jan.  0  /;/  I-IIHIIIKHI  i/r«rs,  Jan.  1  in 
hixxi-j-ti/r  years. 

JTear. 

VIII. 

IX. 

\. 

\l. 

XII. 

Mil. 

XIV. 

Log.  sin  i. 

360°  -  Q. 

1850 

186.5 

.1 

6.12 

19.57 

7.6 

25.<57 

1.2 

8.772211!) 

0          /               // 

284  40     6.9 

1851 

ll().:i 

183 

38.37 

167.22 

27.2 

28.78 

2.0 

2163 

39  31.1 

IN.VJ/;. 

85.2 

76.55 

44.89 

222.51 

6.5 

35.00 

3.5 

2176 

39     1.8 

IN:.:; 

179.6 

203.56 

51.41 

87.80 

45.7 

41.23 

5.0 

2190 

38  29.3 

1854 

103.5 

94.57 

2  1.67 

1N5.44 

5.1 

44.34 

5.8 

2203 

37  56.8 

IN;,;, 

87.4 

222.58 

31.19 

0.73 

11.  li 

50.56 

7.3 

8.7722217 

284  37  21.3 

IS56B. 

172.8 

114.60 

37.70 

66.02 

28.9 

56.78 

s.s 

2230 

36  51.8 

1857 

96.7 

6.61 

10.96 

203.67 

18.5 

59.90 

9.5 

22  1  1 

36   19.3 

1858 

20.5 

133.62 

17.ls 

18.96 

22.7 

6.12 

11.0 

2257 

35    16.  s 

1  s.v.i 

165.0 

24.64 

50.74 

166.60 

42.4 

9.23 

11.8 

2271 

35  14.3 

1860Z?. 

89.8 

168.65 

57.25 

221.89 

21.6 

15.45 

13.3 

8.77222s  1 

284  34  41.7 

1861 

13.7 

(4.66 

:i.77 

37.18 

e.9 

21.68 

14.8 

2298 

31     9.2 

186-2 

158.1 

172.67 

37.03 

IS  1.82 

20.5 

21.79 

15.5 

2311 

33  36.7 

1863 

82.0 

63.69 

43.55 

0.11 

59.7 

31.01 

17.0 

2325 

33     4.2 

1861U. 

6.9 

192.70 

50.07 

55.40 

39.0 

37.23 

18.5 

2339 

32  31.6 

1866 

151.3 

88.71 

23.32 

203.05 

58.6 

40.35 

19.3 

8.7722352 

284  31  59.1 

1866 

75.2 

211.72 

29.84 

18.34 

37.9 

46.57 

20.8 

2366 

31  26.6 

1S67 

219.6 

102.74 

3.10 

165.98 

57.5 

49.69 

21.5 

2379 

30  54.1 

1868J5. 

111.5 

231.74 

9.62 

22  1.27 

36.7 

55.91 

23.0 

2893 

30  21.5 

1869 

68.3 

122.76 

16.13 

36.56 

16.0 

2.13 

21.5 

2406 

29  49.0 

1870 

212.8 

13.78 

1!).39 

181.21 

35.6 

5.24 

25.3 

8.7722  120 

284  29  16.5 

1871 

136.6 

111.7s 

55.91 

239.49 

14.9 

11.47 

26.8 

2  133 

28  44.0 

18725. 

61.5 

83.80 

2.43 

5  1.7!) 

64.1 

17.69 

28.3 

2117 

28  11.5 

1873 

20:>.!> 

161.81 

35.69 

202.43 

13.7 

20.80 

29.1 

2460 

27  39.0 

1S71 

129.8 

52.83 

12.20 

17.72 

53.0 

27.03 

30.6 

2474 

27    6.5 

1875 

53.7 

180.83 

16.46 

165.36 

12.6 

30.14 

31.3 

8.7722487 

284  26  34.0 

1876Z?. 

!!)!).! 

72.85 

21.98 

220.65 

51.9 

36.36 

32.8 

2501 

26     1.4 

1871 

123.0 

200.86 

28.:.() 

35.94 

31.1 

42.59 

34.3 

2515 

25  28.9 

1878 

46.9 

91.87 

1.76 

183.59 

50.7 

45.70 

35.1 

2528 

24  56.4 

1879 

191.3 

219.88 

8.27 

238.88 

30.0 

51.92 

0.6 

25  12 

24  23.9 

18805. 

116.2 

111.90 

14.79 

54.17 

9.2 

58.14 

2.1 

8.7722555 

284  23  51.3 

1881 

40.0 

2.91 

48.05 

201.81 

28.9 

1.26 

2.8 

256!) 

23  18.8 

1882 

1M.:. 

130.92 

54.57 

17.10 

8.1 

7,18 

4.3 

2682 

22  46.3 

1883 

108.3 

21.94 

27.82 

161.75 

27.7 

10.59 

5.1 

2596 

22   13.8 

188  1  /;. 

8&2 

150.95 

31.31 

220.04 

7.0 

16.81 

6.6 

2609 

21  41.2 

1885 

177.6 

41.96 

40.86 

35.33 

462 

23.01 

8.1 

8.7722623 

284  21     8.7 

1886 

101.5 

169.97 

11.12 

182.97 

5.9 

26.15 

8.8 

2636 

20  36.2 

1881 

2:1.  1 

69.99 

20.63 

238.26 

45.1 

82.87 

10.4 

2650 

20    3.7 

18885. 

170.8 

189.99 

27.15 

63.55 

24.4 

38.60 

11.9 

2664 

19  31.1 

1889 

'.)  1.7 

SI.  01 

0.41 

201.19 

44.0 

41.71 

12.6 

2677 

18  58.6 

1N!)0 

is.r, 

209.02 

6.98 

16.48 

23.2 

47.93 

11.1 

8.7722691 

284  18  26.1 

1891 

163.0 

100.01 

40.19 

164.13 

42.9 

51.04 

14.9 

270  1 

17  53.6 

18925 

s7.s 

229.0  1 

46.70 

219.42 

22.  1 

57.27 

16.1 

2718 

17  21.0 

1899 

11.7 

120.06 

63.22 

31.71 

1.4 

3.  If) 

17.9 

2731 

16  48.5 

1894 

156.1 

11.08 

2H.  is 

1  S2.35 

21.0 

6.60 

18.6 

2745 

16  15.9 

1895 

80.0 

139.08 

33.00 

237.64 

0.2 

12.83 

20.1 

8.7722758 

284  15  43.4 

18965 

1.9 

31.10 

89.51 

52  93 

39.5 

19.05 

21.6 

2772 

15   10.8 

1897 

1  19.3 

159.11 

12.77 

200.5* 

nit.  i 

22.16 

22.1 

1  1  ;;s,-{ 

ISDN 

7:1.2 

50.12 

19.29 

16.87 

18.4 

28.39 

23.!) 

27!)!) 

1  1     6.8 

1899 

217.6 

178.13 

52.68 

163.51 

58.0 

81.60 

2  1.6 

(2812 

284  13  33.3 

7  \ 


TABLE    VI. 


Menu  Loiit/i/ittk,  Arguments,  dec.,  for  Washington  Mean  Koon  of  Jan.  0  in  common  years,  Jan.  1  in 
bissextile  years. 

Year. 

I. 

in- 

I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

1900 

0     /     // 

,'M2  IN  55.61 

81 

132.9188 

217.9 

6093 

a 

964 

109.'9 

394.48 

105'!  1 

1901 

207  6  25.31 

83 

48.5173   218.9 

6158   1329 

474.9 

175.55 

226.9 

1902 

71  53  54.99 

84 

188.8165   219.9 

6823   1691 

839.9 

540.55 

105.6 

1903 

296  11  21.67 

86 

104.4150   220.9 

7188 

2059 

1201.9 

321.63 

227.4 

19042. 

163  5  2.15 

88 

21.0131 

221.9 

7554 

2425 

116.0 

103.71 

107.1 

1905 

27  52  31.83 

89 

161.3127 

222.9 

7919 

2790 

481.0 

468.71 

228.9 

1900     25-2  10  1.51 

91 

76.9111 

223.9 

8284 

196 

846.0 

2  19.79 

107.6 

1907 

117  27  31.19 

92 

217.2104  '  221.9 

8649 

561 

1211.0 

30.87 

229.5 

19085. 

343  51  8.67 

91    133.8088 

225.9 

9015 

927 

122.0 

396.87 

109.1 

1909 

208  38  38.35 

96 

49.4073 

226.9 

9380 

1292 

487.0 

177.95 

231.0 

1910 

73  26  8.03 

97 

189.7065 

227.9 

9745 

1657 

852.0 

542.95 

109.6 

1911 

298  13  37.71 

99 

105.3050 

228.9 

10110 

2022 

1217.0 

324.03 

231.5 

19127?. 

164  37  15.20 

101 

21.9034 

229.9 

10476 

2388 

128.1 

106.10 

111.1 

1913 

29  2  t  1  1.N8 

102 

162.2027 

230.9 

10841 

2753 

493.1 

471.10 

233.0 

1914 

2.">l  12  14.56 

104 

77.8011 

231.9 

11206 

158 

858.1 

252.18 

111.6 

1915 

11H  59  11.21 

105 

218.1004 

232.9 

11571 

523 

1223.1 

33.26 

233.5 

19165. 

315  23  21.23 

107 

134.6988 

233.9 

11937 

889 

131.2 

399.26 

113.1 

1917 

210  10  51.11 

109 

50.2973 

234.9 

315 

1251 

499.2 

180.34 

235.0 

1918 

174  58  21.09 

110 

190.5965 

235.9 

680 

1619 

861.2 

515.31 

113.6 

1919 

299  15  50.77 

112 

106.1950 

236.9 

1045 

1984 

1229.2 

326.42 

235.5 

19205. 

166  9  28.26 

114 

22.7935 

237.9 

1411 

2350 

110.2 

108.50 

115.2 

1921 

30  56  57.95 

115 

163.0927 

238.9 

1776 

2715 

505.2 

473.50 

237.0 

1922 

255  44  27.63 

117 

78.6912 

1.0 

2141 

121 

870.2 

25  1.58 

115.7 

1923 

120  31  57.31 

118 

218.9904 

2.0 

2506 

486 

1235.2 

35.65 

237.5 

19B4B. 

346  55  34.80 

120 

135.5889 

3.0 

2872 

852 

146.3 

401.65 

117.2 

1925 

211  43  4.49 

122 

51.1873 

4.0 

3237 

1217 

511.3 

182.73 

239.0 

1926 

76  30  34.17 

123 

191.4866 

5.0 

3602 

1582 

876.3 

547.73 

117.7 

1927 

301  18  3.86 

125 

107.0850 

6.0 

3967 

1917 

1241.3 

328.81 

239.5 

11)287?. 

167  41  41.35 

127 

23.6835 

7.0 

4333 

2313 

152.4 

110.89 

119.2 

1929 

32  29  11.04 

128 

163.9827 

8.0 

4698 

2678 

517.4 

475.89 

2H.O 

1930 

257  16  40.72 

130 

79.5812 

9.0 

5063 

84 

882.4 

256.97 

119.7 

1931 

122  4  10.41 

131 

219.8804 

10.0 

5428 

449 

1247.4 

38.05 

241.5 

19325. 

348  27  47.90 

133 

136.4789 

11.0 

5794 

815 

158.4 

404.05 

121.2 

1933 

213  15  17.59 

135 

52.0774 

12.0 

6159 

1180 

523.4 

185.13 

243.0 

1931 

78  2  47.27 

136 

192.3766 

13.0 

6524 

15-15 

888.4 

550.13 

121.7 

1935 

302  50  16.96 

133 

107.9751 

14.0 

6889 

1910 

1253.4 

331.20 

0.4 

19365. 

169  13  54.46 

140 

24.5735 

15.0 

7255 

2276 

164.5 

113.28 

123.2 

1937 

34  1  24.15 

141 

164.8728 

16.0 

7620 

2641 

529.5 

478.28 

1.9 

1938 

258  48  53.83 

143 

80.4712 

17.0 

7985 

47 

894.5 

259.36 

123.7 

1939 

123  36  23.52  • 

144 

220.7705 

18.0 

8350 

412 

1259.5 

40.44 

2.4 

19405. 

350  0  1.02 

146 

137.3690 

19.0 

8716 

778 

170.5 

406.44 

125.2 

1941 

214  47  30.71 

148 

52.9671 

20.0 

9081 

1143 

535.5 

187.52 

3.9 

1942 

79  35  0.40 

149 

193.2667 

21.0 

9446 

1508 

900.5 

552.52 

125.7 

1943 

304  22  30.09 

151 

108.8651 

22.0 

9811 

1873 

1265.5 

333.60 

4.4 

19445. 

170  46  7.59 

153 

25.4636 

23.0 

10177 

2239 

176.6 

115.68 

127.2 

1915 

35  33  37.28 

154 

165.7628 

24.0 

10542 

2604 

541.6 

480.68 

5.9 

1946 

260  21  6.97 

156 

81.3613 

25.0 

10907 

10 

906.6 

261.76 

127.7 

1947 

125  8  36.66 

157 

221.6606 

26.0 

11272 

375 

1271.6 

42.83 

6.4 

19485. 

351  32  14.16 

159 

138.2590 

27.0 

11638 

741 

182.7 

408.83 

129.2 

1949 

216  19  43.85 

161 

53.8575 

28.0 

15 

1106 

517.7 

189.91 

7.9 

Constant  subtracted  from  L  =  47'  40". 


TABLE   VI. 


M  i-ii  it  I.niKjitiiilf,  Ari/iinii  ills.  i(-c.,/(//-   ]\'«xli!/it//un  Mrmi  \nnit  <,/  Jan.  0  in  common  yriim,  -lini.  1  in 
Itinsi-.rtilf  i/i'Urx. 

iTeor. 

VIII. 

IX. 

Y 

XI. 

XII. 

XIII. 

XIV. 

Log.  sin  /. 

360°-  Q. 

11100 

a 
111.5 

69*15 

59.07 

318.80 

37.2 

87.72 

26.  1 

8.772282  1 

0             /             // 

281    13     O.N 

1901 

65.3 

197.16 

31.09 

16.5 

48.94 

27.6 

2837 

12  2s.:( 

1903 

209.8 

88.n 

88.84 

IN  1.73 

36.  1 

17.0(1 

2s.  1 

2S5  1 

11   55.N 

1903 

183.6 

216.18 

15.36 

237.02 

15.4 

53 

29.9 

2N6  1 

11  23.3 

19017;. 

.-)S.;, 

ios.20 

51.88 

62.81 

54.6 

59.50 

31.1 

281 

10  50.7 

1905 

•JO'.'.il 

236.2  l 

•.'.-..13 

199.96 

11.3 

2.62 

32.2 

8.7722891 

2S|    10    is.-.; 

1906 

126.8 

127.22 

31.65 

15.25 

53.5 

8.84 

33.7 

2905 

9    15.7 

1901 

50.7 

18.24 

i.!n 

162.89 

13.1 

11.95 

3  1.  1 

2918 

1)    13.2 

1908B. 

196.1 

li7.-j:> 

11.48 

2  IS.  18 

52.  1 

18.17 

85.9 

2932 

N    10.6 

1909 

120.0 

38J26 

17.95 

33.  17 

81.6 

21.10 

1.5 

2!)  15 

S     s.  1 

1910 

B.8 

166.27 

51.20 

lsl.12 

51.3 

27.51 

2.2 

8.7722959 

MM     7  35.6 

11)11 

18&8 

5759 

67.72 

236.  1  1 

30.5 

88.78 

3.7 

21)72 

7     3.0 

1912/;. 

113.1 

1SJ.29 

4.24 

61.70 

9.8 

39.96 

5.2 

2986 

(i  30.4 

1913 

37.0 

77.31 

37.  50 

199.3  1 

29.  1 

43.07 

5.9 

2999 

5  57.!) 

19  It 

181.4 

205.32 

11.01 

1  1.63 

8.6 

49.29 

7.1 

3012 

5  -J.Y  1 

1915 

105.3 

96.33 

n.27 

162.27 

558.3 

52.40 

8.2 

8.7723026 

284     4  52.9 

1916B. 

80.2 

225.3  1 

23.79 

217.56 

7.5 

58.63 

9.7 

303!) 

4  20.3 

1917 

174.6 

116.36 

30.3  1 

32.  N5 

46.8 

4.85 

11.2 

3053 

3  -17.H 

1918 

98.5 

7.3S 

3.57 

1N0.50 

(i.  1 

7.96 

11.9 

8066 

3   15.3 

1919 

2&3 

135.:;s 

10.08 

235.79 

45.6 

14.19 

13.4 

3080 

2  42.8 

I90DB. 

1G7.H 

27.40 

16.60 

51.08 

24.9 

20.41 

15.0 

8.7723093 

284     2  10.2 

1921 

91.  (i 

155.11 

49.86 

198.72 

1  1.5 

23.52 

15.7 

3107 

1  37.6 

1922 

15.5 

16.42 

56.38 

11.01 

23.S 

29.75 

17.2 

3120 

1     5.1 

1  923 

159.9 

17-1.13 

29.63 

161.66 

43.4 

32.86 

18.0 

3134 

0  32.6 

19217;. 

848 

66.  15 

36.15 

216.95 

22.6 

39.08 

19.5 

3147 

284     0    0.0 

[925 

8.7 

191.16 

42.67 

32.2  1 

1.9 

45.30 

21.0 

8.7723160 

283  59  27.5 

1926 

153.1 

S5.  17 

15.93 

179.88 

21.5 

48.42 

21.7 

3174 

58  55.0 

11CJ7 

77.0 

213.  is 

22.  15 

235.17 

0.8 

54.64 

23.2 

31K7 

58  22.5 

1928Z?. 

1.9 

105.50 

28.96 

50.46 

40.0 

0.86 

24.7 

3201 

57  49.9 

11)29 

116.3 

233.50 

2.22 

198.10 

59.6 

3.97 

25.5 

3211 

57  17.3 

1930 

70.2 

124.52 

8.74 

13.39 

38.9 

10.20 

27.0 

8.7723228 

283  56  41.8 

1931 

211.  (i 

15.51 

42.00 

161.04 

58.5 

13.31 

27.7 

32  1  1 

56  12.3 

I932J3. 

139.5 

111.55 

48.51 

216.33 

37.8 

19.53 

29.2 

3255 

55  39.7 

19:5:t 

63.3 

35.56 

55.03 

31.62 

17.0 

25.76 

30.7 

3268 

55     7.2 

1934 

207.8 

163.57 

•js.29 

179.26 

36.6 

28.87 

31.5 

3282 

51  34.7 

1936 

131.6 

51.59 

31.81 

231.55 

15.9 

35.09 

33.0 

8.77232!!.") 

283  51     2.1 

193GB. 

56.5 

183.59 

4-1.32 

49.84 

55.1 

11.32 

31.5 

3309 

53  29.5 

19:57 

200.9 

74.61 

i  i..vs 

197.49 

14.8 

44.43 

85.8 

3322 

52  57.0 

1938 

12  1.8 

202.62 

21.10 

12.78 

51.0 

50.65 

0.8 

3335 

52  2-1.5 

1939 

48.7 

93.63 

54.36 

160.42 

13.6 

53.76 

1.5 

3349 

51  52.0 

19405. 

191.1 

222.6  1 

0.88 

215.71 

52.9 

59.99 

3.0 

8.7723362 

283  51   19.4 

1911 

118.0 

113.66 

7.39 

31.00 

32.  1 

6.21 

4.5 

3376 

50  46.9 

1942 

41.8 

4.67 

40.65 

178.64 

51.8 

9.32 

5.3 

3389 

50  11.3 

1913 

186.3 

132.68 

47.17 

233.93 

31.0 

15.55 

6.8 

3403 

49  41.8 

19445. 

111.1 

21.70 

53.69 

•19.22 

10.3 

21.77 

8.3 

3416 

49     9.2 

1945 

35.0 

152.71 

26.95 

196.67 

29.9 

24.88 

9.0 

8.7723430 

283  48  36.7 

1946 

179.4 

43.72 

33.  16 

12.16 

9.1 

31.10 

10.5 

8448 

48     1.2 

1917 

103.3 

171.73 

6.72 

159.80 

28.8 

31.22 

11.3 

31  :.7 

47  31.6 

\'.n-^/:. 

28.2 

63.75 

13.21 

215.09 

8.0 

40.44 

12.8 

3  no 

46  511.0 

1!)19 

172.6 

191.76 

19.76 

30.38 

47.3 

46.66 

14.3 

B.7723484 

2N3    16  26.5 

TABLE   VII. 


Motion  of  mean  Longitude  and  of  —   Q,  ;  and  Fraction  of  Year. 

Common 

Bissextile 

Motion  of  Mran 

.Motion  of 

Fract. 

Year. 

Motion  of  Mran 

Motion  of 

Frart. 

Year. 

Year. 

Longitude. 

3600-  Q 

of  Year. 

Longitude. 

3600-  Q, 

of  Year. 

o     /       /' 

n 

0         /         II 

n 

Jan.     0 

Jan.      1 

0     0     0.00 

—  0.0 

0.000 

Mar.     1 

90     7  48.44 

—  5.3 

0.164 

1 

2 

1   3(j     7.-I 

O.I 

0.003 

2 

97  43  50.25 

5.4 

0.107 

2 

3 

3  12  i.-).i;i 

0.2 

0.005 

3 

99  20     4.05 

5.5 

0.170 

3 

1 

4  48  23.42 

0.3 

0.008 

4 

100  50  11.  8G 

5.6 

0.173 

4 

5 

6  24  3I.'.>3 

—  0.4 

0.011 

5 

102  32  19.07 

—  5.7 

0.175 

5 

6 

8     0  39.04 

0.4 

0.014 

6 

104     8  27.48 

5.8 

0.178 

6 

7 

9  36  4G.K4 

0.5 

0.016 

7 

105  44  35.28 

5.9 

0.181 

7 

8 

11   12  54.05 

0.6 

0.019 

8 

107  20  43.09 

C.O 

0.183 

8 

9 

12  49     2.40 

—  0.7 

0.022 

9 

108  50  50.90 

—  6.1 

0.18C 

g 

10 

14  25  10.27 

0.8 

0.025 

10 

110  32  58.70 

6.1 

0.189 

ID 

11 

1C     1  18.07 

0.9 

0.027 

11 

112     9     0.51 

6.2 

0.192 

11 

12 

17  37  25.88 

1.0 

0.030 

12 

113  45  14.32 

6.3 

0.194 

12 

13 

19  13  33.69 

—  1.1 

0.033 

13 

115  21   22.13 

—  6.4 

0.197 

13 

14 

20  49  41.50 

1.3 

0.030 

14 

11G  57  29.93 

0.5 

0.200 

14 

15 

22  25  49.30 

1.2 

0.038 

15 

118  33  37.74 

0.0 

0.203 

15 

16 

24     1  57.11 

1.3 

0.041 

1C 

120     9  45.55 

6.7 

0.205 

16 

17 

25  38    4.92 

—  1.4 

0.044 

17 

121  45  53.36 

—  6.8 

0.20C 

17 

18 

27  14  12.72 

1.5 

0.047 

18 

123  22     1.16 

0.9 

0.211 

18 

19 

28  50  20.53 

1.6 

0.04!) 

19 

124  58    8.97 

C.9 

0.214 

19 

20 

30  26  28.34 

1.7 

0.052 

20 

126  34  16.78 

7.0 

0.216 

20 

21 

32    2  30.15 

—  1.8 

0.055 

21 

128  10  24.59 

—  7.1 

0.219 

21 

22 

33  38  43.95 

1.9 

0.057 

22 

129  40  32.39 

7.2 

0.222 

22 

23 

35  14  51.70 

2.0 

0.000 

23 

131  22  40.20 

7.3 

0.225 

23 

24 

30  50  59.57 

2.0 

O.OC3 

24 

132  58  48.01 

7.4 

0.227 

24 

25 

38  27    7.38 

—  2.1 

0.000 

25 

134  34  55.81 

—  7.5 

0.230 

25 

26 

40    3  15.18 

2.2 

0.068 

20 

130  11     3.02 

7.6 

0.233 

26 

27 

41  39  22.99 

2.3 

0.071 

27 

137  47  11.43 

7.7 

0.230 

27 

28 

43  15  30.80 

2.4 

0.074 

28 

139  23  19.24 

7.7 

0.238 

28 

29 

44  51  38.00 

—  2.5 

0.077 

29 

140  59  27.04 

—  7.8 

0.241 

29 

30 

46  27  46.41 

2.6 

0.079 

30 

142  35  34.85 

7.9 

0.244 

30 

31 

48     3  54.22 

2.7 

Q.082 

31 

144  11  42.06 

8.0 

0.240 

31 

Feb.     1 

49  40    2.03 

2.8 

0.085 

Apr.     1 

145  47  50.47 

8.1 

0.249 

Feb.     1 

2 

51   10     9.83 

—  2.8 

0.088 

2 

147  23  58.27 

—  8.2 

0.252 

2 

3 

52  52  17.04 

2.9 

0.090 

3 

149     0     C.08 

8.3 

0.255 

3 

4 

54  28  25.45 

3.0 

0.093 

4 

150  30  13.89 

8.4 

0.257 

4 

5 

56     4  33.20 

3.1 

0.096 

5 

152  12  21.C9 

8.5 

0.200 

5 

6 

57  40  41.06 

—  3.2 

0.099 

6 

153  48  29.50 

—  8.5 

0.203 

6 

7 

59  10  48.87 

3.3 

0.101 

7 

155  24  37.31 

8.6 

0.266 

7 

8 

60  52  56.68 

3.4 

0.104 

8 

157     0  45.12 

8.7 

0.2C8 

8 

9 

62  29    4.49 

3.5 

0.107 

9 

158  30  52.92 

8.8 

0271 

9 

10 

64     5  12.29 

-  3.0 

0.110 

10 

160  13    0.73 

—  8.9 

0.274 

10 

11 

05  41  20.10 

3.6 

0.112 

11 

101  49    8.54 

9.0 

0.277 

11 

12 

67  17  27.91 

3.7 

0.115 

12 

163  25  10.:!."> 

9.1 

0.278 

12 

13 

68  53  35.71 

3.8 

0.118 

13 

105     1  24.15 

9.2 

0.282 

13 

14 

70  29  43.52 

—  3.9 

0.120 

14 

106  37  31.96 

—  93 

0.285 

14 

15 

72     5  51.33 

4.0 

0.123 

15 

168  13  39.77 

9.3 

0.288 

15 

10 

73  41   59.14 

4.1 

0.126 

1C 

109  49  47.58 

9.4 

0.890 

16 

17 

75  18    6.94 

4.2 

0.129 

17 

171  25  55.38 

9.5 

0.293 

17 

18 

76  54  14.75 

—  4.3 

0.131 

18 

173    2    3.19 

—  9.G 

0.29G 

18 

19 

78  30  22.56 

4.4 

0.134 

19 

174  38  11.00 

9.7 

0.298 

19 

20 

80    6  30.37 

4.5 

0.137 

20 

170  14  18.80 

9.8 

0.301 

20 

21 

81  42  38.17 

4.5 

0.140 

21 

177  50  26.61 

8.9 

0.304 

21 

22 

83  18  45.98 

—  4.6 

0.142 

22 

179  26  34.42 

—10.0 

0.307 

22 

23 

84  54  53.79 

4.7 

0.145 

23 

181     2  42.23 

10.1 

0.309 

23 

24 

86  31     1.60 

4.8 

0.148 

24 

182  38  50.03 

10.1 

0.312 

24 

25 

88    7    9.40 

4.9 

0.151 

25 

184  14  57.84 

10.2 

0.315 

25 

96 

89  43  17.21 

—  5.0 

0.153 

26 

185  51     5.65 

—  10.3 

0.318 

26 

27 

91    19  25.02 

5.1 

0.150 

27 

187  27  13.46 

10.4 

0.320 

27 

28 

28 
29 

92  55  32.82 
94  31  40.63 

5.2 

—  5.3 

0.159 
0.161 

28 
29 

189    3  21.26 
190  39  29.07 

10.5 
—10.0 

0.323 

0.326 

TABLE  VII. 


Mnl  inn  nf  M,  ,1,1   Lnimiluili'  unit  of  —    Q;  mill  1'rurlinn  ,,f  \'i;ir. 

.M,  ,11011    of 

Uotii 

l-'r.-irtion  of 

«* 

.Motion  of 

.Motion  of 

-.,n  of 

Mran    Longitude. 

-  8 

>  i-.-ir. 

»  i-ar. 

.Mean    Lnngiiinlf. 

-  Q 

0         /         ') 

n 

o       /       // 

II 

April   30 

1.  - 

—  10.7 

Jlllu-  29 

2-  23  y 

—16.0 

0.403 

.May         1 

103  51    41.60 

0.331 

30 

50  33.12 

16.1 

n  r.  6 

2 

195  27  52.4'J 

10.0 

0.334 

July     1 

291    35    10.:  3 

16.9 

(i  i-  - 

3 

197     4      0.30 

10.9 

0.337 

2 

293   11    1-71 

16.3 

0.501 

4 

19"  40     -  II 

—  11  II 

0.340 

3 

291    17  56.55 

—  16  1 

0.504 

."> 

200    Hi   15.91 

11.  1 

0.312 

4 

21     4.35 

li,., 

0.507 

6 

201    52  23.72 

11  2 

0.315 

5 

0   12.16 

16.6 

7 

203  2-  31.53 

11.3 

11.31- 

6 

299  36   19.97 

16.7 

0.512 

8 

205      1  : 

—  11,1 

7 

—  16.7 

0.515 

!) 

-    in    17.14 

1  1  .5 

0.353 

8 

H,  - 

11.51" 

Ill 

116 

0.356 

0 

!   21  43.30 

169 

OJMO 

11 

2,10  53     2.76 

11.7 

(1.359 

10 

0  51.20 

17.1) 

(1.523 

12 

211   29    1 

—11.8 

0.361 

11 

307  36  50.00 

—  17.1 

0.526 

13 

213     5    1 

11.8 

(1.361 

12 

300  13     (i.-l 

172 

14 

214  -II    26.1" 

11.9 

0.367 

13 

310  40   1  1.62 

17.3 

0.531 

15 

216  17  33.90 

12.0 

0.370 

14 

312  25  22.43 

17.1 

0.534 

16 

217  53  41.70 

—12.1 

D.372 

15 

314     1  30.23 

-17  1 

0.537 

17 

210  20  49.60 

12.2 

11.3,75 

16 

315  37  38.04 

17.5 

0.539 

18 

221      5  57.41 

12.3 

0.37" 

17 

317   13    1 

17  6 

0.5  12 

10 

222  42     5.22 

121 

0.381 

18 

318  49  53.66 

17.7 

0.545 

20 

221    1-    13.02 

—  125 

0583 

19 

320  26     1.46 

—17.8 

0.548 

91 

225  51   2.I.-3 

126 

0.386 

20 

:»22     2     0.27 

17.0 

0.550 

22 

227   30  2".6I 

126 

0.389 

21 

323  38  17.08 

18.0 

n,-,:,:', 

23 

229     6  36,15 

12.7 

0.392 

22 

325  14  24.88 

l-i 

0.556 

24 

230  42  41.25 

—12.8 

0.394 

23 

326  50  32.69 

—18.2 

0.550 

25 

232    1"  52.1.6 

12.9 

0.307 

24 

328  26  40.50 

1-2 

0.561 

26 

233  54  59.87 

13.0 

0.400 

25 

330     2  4".31 

1      3 

0.564 

27 

235  31     7.68 

13.1 

0.403 

26 

331  38  56.11 

I  M 

0.567 

28 

237     7  15.48 

-13.2 

0.405 

27 

333  15    3.92 

—18.5 

0.570 

20 

13  23.20 

13.3 

0.408 

28 

334  51    11.73 

18.6 

0.572 

30 

240  10  31.10 

13,1 

0.411 

29 

336  27  19.54 

18.7 

0.678 

31 

241  55  38.90 

134 

0.413 

30 

338     3  27.34 

18.8 

0.578 

June    1 

243  31  46.71 

—13,5 

0.416 

31 

339  39  35.15 

—18.9 

0.580 

2 

245     7  54.52 

13.6 

0.419 

Aug.    1 

341    15  42.06 

19.0 

0.583 

3 

246  44     2.33 

13.7 

0  122 

2 

342  51  50.77 

10.1 

0.686 

4 

248  20  10.13 

13.8 

0.424 

3 

344  27  58.57 

19.1 

0.589 

5 

240  56   17.04 

—13.9 

0.427 

4 

346    4    6.38 

—19.2 

0.591 

6 

251    32  25.75 

14.0 

0.430 

5 

347  40  14.10 

193 

0.594 

7 

253     s  33.56 

14.1 

0.433 

6 

340   Hi  21.00 

191 

0.597 

8 

254  44  41.36 

14.2 

0.435 

7 

350  52  20.80 

19.5 

0.600 

9 

256  20  49.17 

—14.2 

0.438 

8 

352  2-i  37.61 

—19.6 

0.602 

10 

257  56  56.9- 

14.3 

0.411 

9 

351     -I   45.12 

19.7 

0.605 

11 

259  33     4.79 

II  1 

0,111 

10 

355  -III  5322 

I  •  - 

0.6:)8 

12 

261     9  12.50 

11.-, 

0,1  16 

11 

357  17     1.03 

19.9 

0.611 

13 

262  45  20,10 

—14.6 

0.119 

12 

358  53    8.84 

—19.9 

0.613 

14 

261  21   2851 

14.7 

0.452 

13 

0  29  1665 

2  1.0 

0.616 

15 

265  57  36.01 

14.8 

0.455 

14 

2     5  24,15 

BO  1 

0.610 

16 

267  33  43.82 

1  1.9 

0.457 

15 

3  41  32.26 

2,1.2 

0.022 

17 

260     9  51.63 

—  15.0 

0.460 

16 

5  17  40.07 

—20.3 

0.624 

18 

15  5!>,I4 

15.0 

0.463 

17 

6  53  47.88 

20.4 

0.627 

19 

272  22     721 

16.1 

11,165 

18 

8  589  556" 

20.5 

0.630 

20 

273  58  15.05 

15.2 

0.468 

19 

10    6    3.49 

20.6 

0.632 

21 

275  34  22-1, 

-15.3 

0.471 

21) 

11  42  11.30 

—20.7 

0.635 

99 

277  10  30.67 

15.4 

0.474 

21 

13  18  10.10 

20.7 

0.638 

23 

27"  46  38.47 

15.5 

0.476 

22 

1  1  51  26.91 

20.8 

0.641 

24 

280  22  46.28 

15.6 

0.479 

23 

16  30  34.72 

20.9 

0.643 

25 

281  58  54.00 

—  15.7 

0.482 

24 

18     6  42.53 

—21.0 

0.646 

26 

283  35     1  -  ' 

15.8 

n.!-.-, 

25 

19  42  50.33 

21.1 

0.649 

27 

2-5   II      0.70 

15.8 

0.487 

26 

21    IS  5H.I4 

21.2 

0.652 

28 

2^6  47  17.51 

—15.9 

0.490 

27 

22  55     5.95 

—21  .3 

0.6.-,  1 

TABLE  VII. 


Mii/inn  nf  Mi-mi  LoinfiliuJi'  unil  of—  Q;  and  Fraction  of  Yc.nr. 

Vear. 

Motion   (if 

Moan    Longiliido. 

Motion  ni' 
360°—  Q 

Fraction  of 
Year. 

Year. 

Motion  of 
Mean   Longitude. 

Motion  of 
360°—  Q, 

Fraction  of 
Year. 

Aug.  28 

a!  31'  IH'.'TO 

-2l"4 

0.657 

Nov.    4 

o      /       // 
133  28     4.05 

—27.4 

0.843 

"    -J!t 

•Jli     7  21.  .HO 

21  J3 

0.660 

5 

135     4    12.40 

27.5 

0.846 

30 

27  43  29.37 

21.5 

0.663 

0 

130  40  20.27 

27.0 

0.849 

31 

2!)  li)  37.18 

21.6 

0.665 

7 

138  16  28.07 

27.7 

0.852 

Sept.     1 

30  55  44.98 

—21.7 

0.668 

8 

139  52  35.88 

—27.8 

0.854 

2 

32  31  52.79 

21.8 

0.071 

9 

141   28  43.69 

27.9 

0.857 

3 

34     8     0.00 

21.9 

0.074 

10 

143     4  51.50 

28.0 

0.860 

4 

35  44     8.41 

22.0 

0.076 

11 

144  40  59.30 

28.0 

0.862 

5 

37  20  10.21 

—22.1 

0.079 

12 

146  17    7.11 

—  J8.1 

0565 

G 

38  50  24.02 

82,2 

0.682 

13 

147  53   14.92 

28.2 

0.868 

7 

40  32  31.83 

22.3 

0.685 

14 

149  29  22.73 

28.3 

0.871 

8 

42     8  311.04 

22.3 

0.687 

15 

151      5  30.53 

28.4 

0.873 

n 

43  44  47.44 

—22.4 

0.690 

10 

152  41  38.34 

—28.5 

0.876 

10 

45  20  55.25 

22.5 

0.693 

17 

154   17  46.15 

28.6 

0.879 

n 

40  57     3.CG 

22.0 

0.695 

18 

155  53  53.90 

28.7 

0.882 

12 

48  33  10.87 

22.7 

0.098 

19 

157  30     1.70 

28.8 

0.884 

13 

50     9  18.07 

—22.8 

0.701 

20 

159     0     9.57 

—28.8 

0.887 

14 

51  45  26.48 

22.9 

0.704 

21 

100  42  17.38 

28.9 

0.890 

15 

53  21  34.2!) 

S3.0 

0.700 

22 

102  18  25.18 

29.0 

0.893 

16 

54  57  42.09 

23.1 

0.709 

23 

103  54  32.99 

29.1 

0.895 

17 

56  33  49.90 

—23.1 

0.712 

24 

165  30  40.80 

—29.2 

0.898 

18 

58    9  57.71 

23.2 

0.715 

25 

107    6  48.61 

29.3 

0.901 

19 

59  46    5.52 

23.3 

0.717 

26 

108  42  56.41 

29.4 

0.904 

20 

01  22  13.32 

23.4 

0.720 

27 

170  19     4.22 

29.5 

0.906 

21 

02  58  21.13 

—23.5 

0.723 

28 

171  55  1203 

—29.0 

0.91)9 

22 

64  34  28.94 

23.0 

0.720 

29 

173  31   19.84 

29.0 

0.912 

23 

66  10  30.75 

23.7 

0.728 

30 

175     7  27.04 

29.7 

0.914 

24 

07  40  44.55 

23.8 

0.731 

Dec.    1 

176  43  35.45 

29.8 

0.917 

25 

69  22  52.36 

—23.9 

0.734 

a 

178  19  43.26 

—29.9 

0.920 

20 

70  59    0.17 

23.9 

0.737 

3 

179  55  51.07 

30.0 

0923 

27 

72  35     7.98 

24.0 

0.739 

4 

181  31  58.87 

30.1 

0.925 

128 

74  11   15.78 

24.1 

0.742 

5 

183    8    6.68 

30.2 

0.928 

89 

75  47  23.59 

—24.2 

0.745 

6 

184  44  14.49 

—30.3 

0.931 

30 

77  23  31.40 

24.3 

0.747 

7 

186  20  22.29 

30.4 

0.934 

Oct.      1 

78  59  39.20 

24.4 

0.750 

8 

187  56  30.10 

30.4 

0.936 

2 

80  35  47.01 

24.5 

0.753 

9 

189  32  37.91 

30.5 

0.939 

3 

82  11  54.82 

—24.0 

0.756 

10 

191     8  45.72 

—30.6 

0.942 

4 

83  48     2.03 

24.7 

0.758 

11 

192  44  53.52 

30.7 

0.946 

5 

85  24   10.43 

24.7 

0.761 

19 

194  21     1.33 

30.8 

0.947 

6 

87    0  18.24 

24.8 

0.704 

13 

195  57     9.14 

30.9 

0.950 

7 

88  30  20.05 

—24.9 

0.707 

14 

197  33  16.95 

—31.0 

0.953 

8 

90  12  33.80 

25.0 

0.709 

15 

199     9  24.75 

31.1 

0.950 

9 

.     91  48  41.00 

25.1 

0.772 

16 

200  45  32.56 

31.2 

0.958 

10 

93  24  49.47 

25.2 

0.775 

17 

202  21  40.37 

31.9 

0.901 

11 

95     0  57.28 

—25.3 

0.773 

18 

203  57  48.17 

—31.3 

0.964 

12 

90  37    5.08 

25.4 

0.780 

13 

205  33  55.98 

31.4 

0.967 

13 

98  13  12.69 

25.5 

0.783 

20 

207  10     3.79 

31.5 

0.969 

14 

99  49  20.70 

25.6 

0.786 

21 

208  46  11.60 

31.0 

0.972 

15 

101  25  28.51 

—25.0 

0.789 

22 

210  22  19.40 

—31.7 

0.975 

10 

103     1  3031 

25.7 

0.791 

23 

211  58  27.21 

31.8 

0.977 

17 

104  37  44.12 

25.8 

0.794 

24 

213  34  35.02 

31.9 

0.980 

18 

100  13  51.93 

25.9 

0.797 

25 

215  10  42.83 

32.0 

0.983 

1!) 

107  49  59.74 

—26.0 

0.800 

20 

216  46  50.63 

—32.0 

0.986 

20 

109  26     7.54 

20.1 

0.802 

27 

218  22  58.44 

32.  1 

0.988 

21 

111     2  15.35 

20.2 

0805 

28 

219  59     6.25 

32.2 

0.991 

22 

112  38  23.16 

26.3 

0.808 

29 

221  35  14.06 

32.3 

0.994 

33 

114  14  30.97 

—26.4 

0.810 

30 

223  11  21.86 

—32.4 

0.997 

24 

1  1  5  50  38.77 

20.4 

0.813 

31 

224  47  29-6? 

32.5 

0.999 

25 

117  26  40.58 

26.5 

0.816 

32 

226  23  37.48 

32.0 

1  .002 

20 

119     2  54.39 

20.0 

0.819 

33 

227  59  45.28 

32.7 

1.005 

27 

120  39     2.19 

-20.7 

0.821 

34 

229  35  53.09 

—32.8 

1  .008 

28 

122  15  10.00 

20.8 

0.824 

35 

231    12     0.90 

32.8 

1.010 

30 

123  51   17.81 

20.9 

0.827 

30 

232  48     8.71 

32.0 

1.013 

30 

125  27  25.62 

27.0 

0.830 

37 

234  24  16.51 

—33.0 

1.010 

SI 

127     3  33.42 

—27.1 

0.832 

Nov.     1 

128  39  41.23 

27.2 

0.835 

2 

130   15  49.04 

27.2 

0.838 

3 

131   51   W^, 

—27.3 

0.84  1 

TABLE   VIII. 


17 


Mi'liiHI   <>/'    Mrilll    I.  n  II  -ri  hi,  If. 

Hours. 

For  Hours. 

.Minn 
Hecondi. 

For  .Mimitrs. 

Ollcls. 

.Mi  nut 

.inU. 

For  Jliinr 

For  Si'i'oinls. 

1 

o       /     // 

0     l  0.325 

1 

/       // 
0      1.005 

0.067 

31 

/       // 

2      1.168 

8,'o69 

•1 

0      8    0.651 

g 

(1        S.OH 

0.134 

32 

2     S.I  73 

2.136 

3 

0    12  O.!l7(i 

3 

0    12.016 

0.200 

33 

2    12.17!) 

-.'203 

1 

0   Hi    l.:i()l 

I 

0    16.022 

0.2(17 

31 

2    16.  1M 

2.270 

:. 

0  20   1.627 

5 

0  20.027 

0.331 

35 

2  20.11)0 

2.336 

6 

0  21    1.952 

<i 

0  21.033 

0.101 

36 

2  21.195 

2.  103 

7 

0  28  2.277 

7 

0  28.038 

0.  167 

87 

2   -js.201 

2.170 

8 

0  32  2.602 

8 

0  32.013 

0.534 

:is 

2  32.206 

2.687 

!» 

0  36  2.M28 

!) 

0  36.01!) 

0.601 

39 

2  36.211 

2.601 

10 

0  40  3.253 

10 

(1    10.051 

6.688 

40 

2    10.217 

2.670 

11 

o  H  3.57s 

11 

0    II.  Olid 

0.731 

41 

2    1  1.222 

2.737 

13 

0    is   :j.!KI| 

12 

0    IS.  (Ml.-) 

0.801 

12 

2    ls.228 

2.801 

ia 

0  52    1.22!) 

ia 

0  52.070 

0.868 

43 

2  52.233 

2.871 

11 

o  56  i.55i 

11 

0  56.07  U 

0.936 

1! 

2  56.239 

2.1)37 

15 

1     0    1.8SO 

15 

1       0.081 

.001 

15 

3     0.2  1  1 

3.001 

it; 

1    i  5.205 

16 

1.0S7 

.Oils 

III 

3      1.219 

3.071 

17 

N  5.530 

17 

8.092 

.185 

17 

3     s.  •„>.->.-> 

3.138 

18 

12  5.856 

18 

12.098 

.202 

IS 

3    12.260 

3.204 

1!) 

lii    (J.181 

19 

16.103 

.268 

49 

3    16.266 

3.27  1 

•JO 

20  6.50(i 

20 

20.108 

.388 

50 

3  20.271 

3.3 

21 

21  6.831 

21 

24.114 

.102 

51 

3  21.277 

3.  105 

22 

28  7.157 

22 

1   28.119 

.469 

52 

3  2N.282 

3.171 

23 

:!2  7.182 

23 

1   32.125 

.536 

63 

3  32.287 

3.5  !'  i 

21 

36  7.N07 

21 

1  36.130 

.602 

51 

3  36.293 

3.605 

25 

1  40.136 

1.869 

55 

3    10.21)8 

3.672 

26 

1  44.141 

1.736 

56 

3    11.301 

3.738 

27 

1    IN.  116 

1.802 

57 

3    18.309 

3.N05 

28 

1   52.152 

1.869 

58 

3  52.314 

3.872 

29 

1  56.157 

1.936 

59 

3  56.320 

8488 

30 

2     0.163 

2.003 

60 

4     0.325 

4.005 

Days.                      Motion  of  M.  L. 

Days. 

Motion  of  M.  1..                     Days. 

Motion  of  M.  L. 

0.1                     09  36"781 

0.01 

.  o'  5T678                    0.001 

5^768 

0.2                    0  19  13.561 

0.02 

1  55.356                     0.002 

11.536 

0.3                       0  '28  50.312 

0.03 

2  53.034                       0.003 

17.303 

0.4                     0  38  27.123 

0.04 

3  50.712                     0.004 

23.071 

0.5                     0  48     :i.!)()l 

0.05 

4  48.390                    0.005 

88.889 

0.6                     0  57  40.(i>  1 

0.06 

5  46.068                    0.006 

31.607 

0.7                      1     7   17.465 

0.07 

6  43.746                    0.007 

40.375 

0.8                      1   16  51.216 

0.08 

7  41.125                     0.008 

46.112 

0.9                      1  26  31.027 

0.09 

H  31).  103                     0.009 

51.910 

1.0                      1  36     7.807 

0.10 

9  36.781                      0.010 

57.678 

TABLE  IX. 

Factor  of  a  small  Correction  to  be  multiplied  by  the  fraction  of  the  year  and  then  added  to  L. 

Vfiir.                  Factor. 

r««r. 

Factor. 

Year.                 Factor. 

Year. 

Fin  tor. 

1750              -O'blS 

1800 

-o'bn 

1850              —  O'OOS 

1900 

+o'.007 

1760                 0.016 

1810 

0.010 

l.s:;o               0.003 

1910 

0.010 

1770                 0.015 

1820 

0.009 

1870             -0.001 

1920 

0.013 

17sO                  0.014 

1830 

0.007 

JNMI             +0.001 

1930 

0.016 

17!)0                  0.012 

1840 

0.006 

1890                 0.001 

1940 

0.020 

1800              -0.011 

1850 

-0.005 

1900             +0.007 

1950 

+0.088 

18 


TABLE    X. 


EQUATION  OF  THE  CENTRE,  FOR  111  =  0. 

d 

Constant  added  47'  3".5.     Period  =  224.7008. 

d 

Diff. 

d 

Diff. 

d 

Diff. 

d 

Diff. 

d 

Diff. 

Arg.  I.  !            O.O 

for  0<l.l 

0.1 

for  U'l.l 

O.2 

for  0-1.1 

0.3 

for  O-i.l 

O.4 

fur  (J'l.l 

6     1     047     »5() 

// 
+7.96 

47'  MAG 

u 
+7.96 

47'  19.42 

ii 
+7.96 

47  27.38 

u 
+7.96 

47  3f>.35 

n 
+7.96 

1     |     0  48  2*1  1 

7.96 

48  31.07 

7.96 

48  39.03 

7.96 

48  40.98 

7.96 

48  54.!  14 

7.95 

2     i     04!)  42.05 

7.95 

49  50.00 

7.95 

4!)  58.55 

7.95 

50    0.50 

7.94 

50  14.44 

•  7.94 

3 

0  51    2.07 

7.93 

51  10.00 

7.93 

51  17.93 

7.93 

51  25.86 

7.93 

51  33.79 

7.92 

4 

0  52  21.30 

7.91 

52  29.21 

7.91 

52  37.11 

7.91 

52  45.02 

7.00 

52  52.92 

7.90 

5 

0  53  40.27 

7.88 

53  48.15 

7.88 

53  50.02 

7.88 

54     3.90 

7.87 

54  11.77 

7.87 

(i 

0  54  58.92 

7.85 

55    0.77 

7.84 

55  14.61 

7.84 

55  22.44 

7.1  1 

55  30.28 

7.83 

7 

0  50  17.19 

7.81 

50  25.00 

7.80 

50  32.79 

7.80 

56  40.59 

7.79 

50  48.38 

7.79 

8 

0  57  35.02 

•7.76 

57  42.78 

7.75 

57  50.53 

7.75 

57  58.27 

7.74 

58    0.01 

7.74 

0 

0  58-52.34 

7.70 

59    0.04 

7.70 

59    7.74 

7.69 

59  15.43 

7.69 

59  23.11 

7.68 

10 

1     0    9.09 

7.li  1 

0  10.74 

7.64 

0  24.37 

7.63 

0  32.00 

7.63 

0  39.02 

7.88 

11 

1     1  25.22 

7.08 

1  32.79 

7.57 

1  40.30 

7.56 

1  47.92 

7.56 

1  55.48 

7.55 

12 

1     2  40.05 

7.01 

2  48.15 

7.50 

2  55.05 

7.49 

3    3.14 

7.48 

3  10.02 

7.48 

13 

1     3  55.33 

7.43 

4     2.70 

7.42 

4  10.17 

7.41 

4  17.58 

7.40 

4  24.98 

7.40 

14 

1     5     9.20 

7.31 

5  10.54 

7.34 

5  23.88 

7.33 

5  31.20 

7.32 

5  38.51 

7.31 

15 

1     0  22.21 

7.20 

6  29.40 

7.24 

0  30.70 

7.24 

6  43.93 

7.23 

6  51.15 

7.22 

16 

1     7  34.28 

7.16 

1  41.44 

7.15 

7  48.58 

7.14 

7  55.71 

7.13 

8    2.84 

7.12 

17 

1     8  45.37 

7.l)(i 

8  52.43 

7.05 

8  59.47 

7.04 

9    0.50 

7.03 

9  13.52 

7.01 

18 

1     9  55.12 

MB 

10    2.37 

6.94 

10     9.30 

6.93 

10  10.22 

6.92 

10  23.14 

6.1)1 

19 

1  11     4.37 

O.bl 

11  11.20 

6.63 

11  1S.03 

C.82 

11  24.83 

6.80 

11  31.03 

6.79 

20 

1  12  12.17 

6.72 

12  18.89 

6.71 

12  25.59 

6.70 

12  32.28 

6.68 

12  38.9(  i 

6.67 

21 

1  13  18.77 

6.60 

13  25.36 

6.58 

13  31.94 

6.57 

13  38.50 

6.56 

13  45.0(  i 

6.55 

22 

1  14  24.10 

6.47 

14  30.57 

6.46 

14  37.02 

6.44 

14  43.45 

6.43 

14  49.87 

6.42 

23 

1  15  28.13 

6.34 

15  34.46 

6.32 

15  40.78 

6.31 

15  47.08 

6.29 

15  53.36 

6.28 

24 

1  10  30.80 

6.20 

16  36.99 

6.19 

16  43.10 

6.17 

16  4!  1.32 

6.10 

16  55.47 

6.14 

25 

1  17  32.05 

6.05 

17  38.10 

6.04 

17  44.13 

6.02 

17  50.15 

6.01 

17  50.15 

6.00 

20 

1   18  31.85 

5.90 

18  37.75 

5.89 

18  43.03 

5.87 

18  49.50 

5.86 

18  55.35 

5.84 

27 

1  19  30.15 

0.70 

19  35.89 

5.74 

19  41.02 

5.72 

19  47.33 

5.71 

19  53.03 

5.69 

28 

1  20  20.89 

5.59 

20  32.47 

0.58 

20  38.05 

5.56 

20  43.60 

0.00 

20  49.14 

5.53 

29 

1  21  22.04 

5.4:1 

21  27.46 

5.'I2 

21  32.87 

5.40 

21  38.20 

5.38 

21  43.04 

5.37 

30 

1  22  15.55 

5.27 

22  20.81 

5.25 

22  20.05 

5.23 

22  31.27 

5.21 

22  36.48 

5.20 

31 

1  23    7.38 

5.10 

23  12.47 

5.08 

23   17.54 

5.06 

23  22.59 

0.00 

23  27.63 

5.03 

32 

1  23  57.49 

4.92 

24    2.40 

4.90 

24     7.30 

4.89 

24  12.18 

4.87 

24  17.04 

4.83 

33 

1  24  45.84 

4.75 

24  50.58 

4.73 

21  55.29 

4.71 

25     0.00 

4.09 

25     4.08 

4.07 

34 

1  25  32.39 

4.56 

25  30.95 

4.05 

25  41.49 

4.03 

25  40.00 

4.01 

25  50.50 

4.49 

35 

1  26  17.12 

4.38 

20  21.49 

4.36 

20  25.84 

4.34 

26  30.17 

4.32 

20  34.49 

4.30 

30 

1  20  59.97 

4.19 

27    4.15 

4.17 

27    8.32 

4.15 

27  12.40 

4.13 

27  16.59 

4.11 

37 

1  27  40.93 

4.00 

27  44.92 

3.98 

27  48.89 

3.96 

27  52.84 

3.94 

27  50.77 

3.92 

38 

1  28   19.90 

3.80 

28  23.75 

3.78 

28  27.53 

3.77 

28  31.28 

3.75 

28  35.02 

3.73 

39 

1  28  57.02 

3.61 

29     0.02 

3.59 

29    4.20 

3.57 

29    7.70 

3.55 

29  11.29 

3.53 

40 

1  29  32.10 

3.41 

29  35.50 

3.39 

29  38.87 

3.37 

29  42.23 

3.35 

29  45.57 

3.33 

41 

1  30    5.10 

3.20 

30    8.30 

3.18 

30  11.53 

3.16 

30  14.09 

3.14 

30  17.82 

3.12 

49 

1  30  30.19 

3.00 

30  39.18 

2.98 

30  42.14 

2.90 

30  45.09 

2.94 

30  48.02 

2.92 

43 

1  31     5.15 

2.79 

31     7.93 

2.77 

31  10.09 

2.70 

31   13.43 

2.73 

Jl    10.15 

2.71 

44 

1  31  32.02 

2.58 

31   31.59 

2.56 

31  37.15 

2.04 

31  39.08 

aja 

31  42.18 

2.00 

45 

1  31  50.80 

2.37 

31  59.10 

2.35 

32     1.50 

2.33 

32    3.81 

2.31 

32    6.11 

2.29 

46 

1  32  19.45 

2.16 

32  21.59 

2.14 

32  23.72 

2.12 

32  25.83 

2.09 

32  27.91 

2.07 

47 

1  32  39.90 

l.ill 

32  41.89 

1.92 

32  43.80 

1.90 

32  45.09 

1.87 

32  47.50 

1.85 

48 

1  32  58.32 

1.73 

33    0.04 

1.71 

33     1.73 

1.68 

33    3.40 

1.66 

33     5.00 

1.04 

49 

1  33  14.51 

1.51 

33  10.01 

1.49 

33  17.19 

1.47 

33  18.95 

1.44 

33  20.38 

1.42 

50 

1  33  28.53 

1.29 

33  29.81 

1.27 

33  31.07 

1.25 

33  32.30 

1.23 

33  33.52 

1.20 

51 

1  33  40.30 

1.08 

33  41.42 

1.05 

33  42.40 

1.03 

33  43.48 

1.01 

33  44.47 

0.99 

52 

1  33  49.99 

0.85 

33  50.83 

0.83 

33  51.05 

0.81 

33  52.45 

0.79 

33  53.23 

0.76 

59 

1  33  57.13 

0.63 

33  58.or, 

O.lil 

33  58.05 

0.09 

33  59.23 

0.06 

33  59.78 

0.54 

54 

1  34     2.00 

0.11 

34    3.00 

(1.39 

34     3.11 

0.37 

31     3.80 

0.35 

31     4.13 

0.32 

55 

I  34    5.08 

+0.19 

3  1     5.80 

+0.17 

31    0.02 

+:i.io 

34    0.15 

+0.13 

34     0.27 

+0.10 

TABLE   X. 


EQUATION  OF  TIIF.  (TATKF..   FOU  111=0. 

.1 

(•..nstimt   ;„!,!.  •,!    IT'  :;"  .:,.      IVrio.l  WM  221  : 

d 

Diff. 

,1 

Diff. 

.1 

Diff. 

.1 

Diir. 

d 

Diff. 

Arg.I. 

0.5 

fur  I*'1.  1 

0.8 

0.7 

f..r  U.I.I 

0.8 

f.,r  (I'M 

<>.!» 

furll'i.l 

d 
0 

0    17    43.31 

II 

IT-  51.27 

n 

47   5:i23 

ii 
+7.96 

481    7'.'l9 

n 
+7.% 

4^  15'J5 

n 

1 

0    19     2.-H 

lit   in..-:, 

7.95 

49    l-.-ll 

49  20.75 

TJt 

49  31.70 

7.95 

a 

0  :,(i  22.38 

50  :  10.32 

7.94 

50  3-.20 

50  40.20 

7Jt 

50  51.1  1 

7.1i:i 

3 

0  :.l    11.71 

51    19.03 

51    57.55 

52     5.17 

52    I3.3S 

7.DI 

4 

0  53    o.s-> 

7.90 

53     -.7  1 

7.89 

53    10.01 

7.89 

53  21.50 

7.89 

53  32.38 

7.88 

:. 

0  51    19.01 

7.86 

51  27.50 

7.86 

51  35.30 

51   43.22 

54  51.07 

us 

o 

0  55  :l-.l  1 

. 

55    15.!  '3 

55  53.75 

50     1.57 

50     9.3* 

',.-1 

7 

0  50  50.10 

7.78 

57     3.95 

7.78 

57   11.72 

7.77 

57   lit.  lit 

7.77 

57  27.20 

tM 

8 

n  5-i   13.75 

7.73 

5<  21.1- 

7.73 

'  '.20 

7.7-_> 

")"*     *{l  t  '  t"' 

7.72 

58  44.1.1 

7.71 

9 

n  59  30.79 

7.67 

59  3>.  10 

7.117 

59  40.13 

59  53.79 

7.66 

00     1.44 

1M 

10 

1     0  47.21 

7.1!  1 

0  51.S5 

7.01 

1      2.  15 

7.60 

1    10.H5 

. 

1    17.01 

7-r,8 

11 

1     2    3.02 

;  ..  >  i 

2  10.50 

• 

2    is.  |0 

7.53 

2  25.02 

2  It!.  II 

7.51 

12 

1      3    IS.Oil 

7,17 

3  25.55 

7.16 

3  .33.01 

7,1.-, 

3  40.46 

7.44 

3  47.90 

7.44 

13 

1     4  32.37 

7.39 

4  39.71  i 

7.38 

1    17J3 

7.37 

I  51.50 

7.36 

5     I,-?, 

7  JO 

14 

5  45.S2 

7.30 

5  53.11 

7.-3D 

0     0,10 

7.28 

0    7.08 

7.27 

0   11.95 

7.26 

15 

0  5S.30 

7JM 

7    5.57 

7.20 

7  12.70 

7.19 

7  lit.!  14 

7.18 

7  27.12 

7.17 

10 

8     it.!  15 

7.11 

8  17.06 

7.10 

8  24.15 

7.09 

8  31.24 

7.08 

8  38.31 

7.07 

17 

it  20.53 

7.00 

9  27.53 

6.99 

it  31.52 

6.98 

it  41.50 

6.97 

9    IS.  17 

6.96 

18 

10  30.04 

6.90 

10  30.!  13 

6.88 

10  43.-  1 

6.87 

10  50.07 

6.86 

10  57.53 

6.85 

19 

11  3-.  12 

6.78 

11  45.19 

6.77 

11  51.96 

6.76 

11  58.71 

6.74 

12    5,15 

6.73 

20 

1    12  45.H3 

6.66 

12  52.28 

tM 

12  :>-'.:  >2 

6.63 

13    5.55 

6.63 

13  12.17 

6.61 

21 

1   13  51.00 

m 

13  5s.  12 

6.53 

II        I.OI 

6.51 

11   11.14 

6.50 

14  17.03 

6.48 

2-.' 

1   14  50.2s 

6.40 

15    2.0S 

6.39 

15    9.00 

6.38 

15  15.43 

6.36 

15  21.79 

6.35 

23 

1  15  59.01 

6.37 

16    5.90 

10   12.11 

tM 

16  18.38 

6.23 

10  24.59 

6.21 

21 

1  17     1.00 

6.13 

17     7.72 

6.11 

17  13.S3 

6.10 

17  19.92 

6.08 

17  25.!  til 

6.07 

25 

1    IS     2.11 

5.98 

18    s.ll 

5.96 

18  14.07 

5.95 

18  20.01 

5.93 

18  25.91 

Ml 

26 

1     19       1.19 

5.83 

19     7.01 

5.81 

lit   12.-2 

5.80 

19    IS.OI 

5.78 

lit  24.39 

5.77 

27 

1    lit  r,-.7  1 

5.67 

20    4.38 

5.66 

20  10.03 

5.64 

20  15.07 

5.63 

20  21.29 

5.01 

28 

1  20  51.00 

5.52 

21     0.17 

5.50 

21     5.00 

5.48 

21  11.14 

5.47 

21  16.60 

.-,.  I.1. 

29 

1  21  49.00 

5.35 

21  51.31 

5.33 

21  59.07 

U| 

22    4.!  is 

5.30 

22  10.27 

5.38 

30 

1  22  41.07 

5.18 

22  40.85 

5.16 

22  52.01 

5.15 

22  57.15 

5.13 

23    2.27 

5.11 

31 

1  23  32.05 

5.01 

23  37.65 

4.1111 

23  42.64 

4.98 

23  47.60 

4.96 

23  52.55 

4.94 

32 

1  21  21.88 

4.83 

24  20.71 

4.83 

24  31.52 

4.80 

21  30.31 

4.78 

24  41.08 

4.76 

33 

1  25    9.34 

4.66 

25  13.rut 

4.64 

25  1S.02 

4.63 

25  23.23 

4.60 

25  27.82 

4.58 

31 

1   25  51.99 

4.47 

25  59,15 

4.45 

20     3.S9 

4.43 

20     S.32 

4.42 

26  12.73 

4  .XI 

35 

1  20  38.78 

4.38 

20  43.00 

4.27 

26  47.31 

4.a:i 

26  51.55 

4.23 

26  55.77 

4.31 

36 

1  27  20.0!  i 

4.09 

27  24.78 

4.08 

27  28.84 

4.06 

27  32.S9 

4.04 

27  36.92 

4.03 

1  28     0.09 

3.90 

28     4.5s 

3.88 

28    8.45 

3.86 

28  12.31 

3.84 

28  10.14 

3.82 

38 

1   2-  3S.7I 

3.71 

28  42.43 

3.69 

28  40.11 

3.67 

28  49.77 

3.65 

28  .53,10 

3.63 

39 

1  29  14.81 

3.51 

29  18.31 

3.49 

29  21.79 

3.47 

29  25.25 

3.45 

29  28.68 

3.43 

40 

1  29.48.88 

3.31 

29  52.18 

3.29 

29  55.  Hi 

3.37 

29  5S.71 

3.35 

30     1.95 

3.32 

41 

30  20.93 

3.10 

30  24.02 

3.08 

30  27.0!  t 

3.06 

30  30.15 

3.04 

30  :t3.I8 

3.02 

49 

30  5!  1.93 

2.90 

30  53.S1 

3.88 

30  50.0S 

30  59.52 

3.83 

31     2.31 

3.81 

43 

31  18.85 

2.69 

31  21.52 

2.67 

31  24.18 

MB 

31  26.81 

Ml 

31  29.43 

3.60 

44 

31  41.07 

2.48 

31  47.14 

2.46 

31  49.5!  1 

2.44 

31  52.01 

3.41 

31  51.11 

2.39 

10 

32     S.39 

2.27 

32  lo.oi 

3.34 

32  12.88 

32  15.09 

2.20 

32   I7.2S 

2.18 

46 

32  29.97 

2.05 

32  32.01 

2.03 

32  34.03 

3.01 

32  30.03 

1.99 

32  38.00 

1.97 

47 

32  49.11 

1.83 

32  51.23 

1.81 

32  53.04 

1.79 

32  54.82 

1.77 

32  56.58 

1.75 

48 

33    0.09 

1.63 

:«     S.29 

1.60 

33    9.88 

1.58 

33  11.45 

1.55 

33  12.99 

1.53 

49 

3-3  21.79 

1.40 

33  23.  IS 

1.38 

33  24.55 

1.36 

33  25.90 

1.34 

33  27.22 

1.31 

50 

:«  34.71 

1.18 

33  35.S9 

1.16 

33  37.04 

1.14 

a3  38.16 

1.13 

33  8!  1.27 

1.10 

51 

33  45.15 

0.96 

:(3  40.40 

0.94 

33  47.:i3 

0.93 

S3  4s.21 

0.90 

33  49.13 

0.88 

52 

33  53.9S 

0.74 

33  51.72 

0.72 

33  55.13 

0.70 

33  50.11 

0.67 

33  50.7  s 

Ml 

53 

34    0.32 

0.52 

34     (),-"{ 

O..V) 

31     1.32 

0.48 

31      1.79 

0.46 

31     2.23 

0.43 

'     51 

31      l.ll 

0.30 

31      1.73 

0.28 

31     5.00 

0.26 

31     5.25 

0.34 

31     5.  IS 

+0.-J1 

55 

31     0.36 

40.08 

34    0.13 

31     0.48 

.  i."l 

34    0.50 

+0.01 

34    6.51 

-0.01 

8  V 


TABLE    X. 


EQUATION  OF  THE  CENTRE,  FOR  in  =  0. 

d 

Constant  added  47'  3".5.     Period  =  224.7008. 

d 

Diff. 

d 

Diff. 

d 

Dim 

d 

Diff 

d 

Dim 

Arg.  I. 

o.o 

for  0<U 

O.I 

for  0>U 

o.a 

for  O''.l 

0.3 

forO'U 

0.4 

for  IK  1 

56 

0          1          II 

1  31     6.49 

-0.03 

34    o!-!5 

-0.05 

31     0.39 

II 
-0.07 

34    6.31 

-0.09 

34     0.20 

ii 
-0.12 

57 

1  34     5.10 

0.25 

34     4.  si 

II.-J7 

34     4.50 

0.39 

34     4.25 

0.32 

34     3.92 

o.:i  i 

58 

1  31     1.50 

0.47 

34     1.02 

0.19 

34     0.52 

0.51 

33  59.99 

0.54 

33  59.45 

0.56 

59 

J  33  55.71 

0.69 

33  55.01 

0.71 

33  54.28 

0.73 

33  53.54 

0.75 

33  52.77 

0.78 

60 

1  33  47.72 

0.91 

33  46.80 

0.93 

33  45,-;  i 

0.95 

33  44.89 

0.97 

33  43.91 

1.00 

lil 

1  33  37.54 

1.13 

33  30.10 

1.15 

33  35.24 

1.17 

33  34.06 

1.10 

33  32.86 

1.21 

02 

1   33  25.19 

1.34 

33  23.83 

1.37 

33  22.45 

1.39 

33  21.06 

1.41 

33  19.64 

1.43 

03 

1   33  10.67 

1.56 

33    9.10 

1.5S 

33     7.51 

1.60 

33    5.89 

1.62 

33     4.26 

1.65 

01 

I  32  54.00 

1.77 

32  52.21 

1.80 

32  50.41 

1.82 

32  48.58 

1.84 

32  40.73 

1.86 

05 

1  32  35.19 

1.99 

32  33.19 

2.01 

32  31.17 

2.03 

32  29.13 

2.05 

32  27.07 

2.07 

ot; 

1   32   1  1.26 

2.20 

32  12.05 

8.99 

32    9.82 

2.24 

32    7.57 

2.26 

32    5.29 

2.28 

07 

1  31  51.22 

•J.tl 

31  48.80 

3.43 

31  40.37 

2.45 

31  43.91 

2.47 

31  41.42 

2.49 

08 

1  31  26.10 

2.63 

31  23.48 

-  2.64 

31  20.83 

2.66 

31  18.16 

2.68 

31   15.47 

2.70 

69 

1  30  58.92 

2.83 

30  50.09 

2.84 

30  53.23 

2.86 

30  50.36 

2.88 

30  47.47 

SUM 

70 

1  30  29.09 

3.03 

30  20.06 

3.04 

30  23.00 

3.06 

30  20.53 

3.08 

30  17.43 

3.10 

71 

1  29  58.15 

3.33 

29  55.21 

3.24 

29  51.90 

3.20 

29  4S.OS 

3.28 

29  45.39 

3.30 

72 

i  29  •>.->.•:  i 

3.43 

29  21.78 

3.44 

29  18.33 

3.46 

29  14.86 

3.48 

29  11.37 

s.r.o 

73 

1   28  50.01 

3.62 

28  46.38 

3.64 

28  42.74 

3.66 

28  39.07 

3.68 

28  35.39 

3.69 

74 

1  28   12.87 

3.81 

28    9.05 

3.83 

28    5.22 

3,85 

28     1.36 

3.87 

27  57.18 

3.89 

75 

1  27  3:  (..-.( 

4.00 

27  29.82 

4.02 

27  25.79 

4.04 

27  21.75 

4.05 

27  17.68 

4.07 

76 

1  20  52.91 

4.18 

26  48.71 

4.30 

26  44.50 

4.32 

20  40.27 

4.24 

26  36.02 

4.26 

77 

1  26  10.14 

4.37 

26    5.77 

4.38 

26     1.37 

4.40 

25  50.96 

4.42 

25  52.53 

•5.44 

78 

1  25  25.57 

4.55 

25  21.02 

4.56 

25  16.44 

4.58 

25  11.85 

4.60 

25    7.24 

4.62 

79 

1  24  39.23 

4.72 

24  31.50 

4.74 

24  29.75 

4.76 

24  24.98 

4.77 

24  20.20 

4.79 

80 

1  23  51.14 

4.89 

23  46.24 

4.91 

23  41.32 

4.93 

23  30.39 

4.94 

23  31.43 

4.96 

81 

1  23     1.36 

5.06 

22  50.29 

5.08 

22  51.21 

5.09 

22  46.10 

5.11 

22  40.98 

5.13 

82 

1  22     9.92 

5.23 

22    4.0!) 

5.34 

21  59.44 

5.26 

21  54.17 

5.27 

21  48.89 

SM 

83 

1  21  10.86 

5.39 

21   11.47 

5.40 

21     6.06 

5.42 

21     O.(i3 

5.43 

20  55.19 

5.45 

84 

1  20  22.23 

5.54 

20  10.08 

5.56 

20  11.12 

5.57 

20    5.54 

5.59 

19  59.94 

5.60 

85 

1    19  20.00 

5.69 

19  20.36 

5.71 

19   14.64 

5.72 

19     8.91 

5.74 

19.    3.17 

5.75 

86 

1  18  28.39 

5.84 

18  22.55 

5.85 

IS   10.69 

5.87 

18  10.81 

5.88 

18    4.92 

5.90 

87 

1  17  29.29 

5.98 

17  23.30 

5.99 

17  17.30 

6.01 

17  11.28 

6.03 

17    5.25 

6.04 

88 

1  10  28.78 

6.12 

16  22.65 

6.13 

1C  10.51 

6.15 

16  10.36 

6.16 

16    4.19 

'   6.18 

89 

1  15  20.92 

6.25 

15  20.06 

6.26 

15  14.39 

6.28 

15    8.10 

6.29 

15     1.81 

6.30 

90 

1  14  23.75 

6.38 

14  17.37 

6.39 

14  10.97 

6.40 

14     4.50 

6.42 

13  58.13 

6.43 

91 

1  13  19.33 

6.50 

13  12.82 

6.51 

13    0.30 

6.53 

12  59.77 

6.54 

12  53.22 

6.55 

92 

1   12  13.70 

6.62 

12    7.08 

6.63 

12    0.44 

6.64 

11  53.79 

6.66 

11  47.13 

6.67 

93 

1  11     6.92 

6.73 

11     0.18 

6.75 

10  53.43 

6.76 

10  40.07 

6.77 

10  39.89 

6.78 

94 

1     9  59.03 

6.84 

9  52.19 

6.85 

9  45.33 

6.86 

9  38.40 

6.87 

9  31.58 

6.88 

95 

1     8  50.09 

6.94 

8  43.14 

6.95 

8  30.18 

6.96 

8  29.22 

6.97 

8  22.24 

6.98 

96 

1     7  40.16 

7.04 

7  33.11 

7.05 

7  20.05 

7.06 

7  18.99 

7.07 

7.11.91 

7.08 

97 

1     6  29.27 

7.13 

6  22.14 

7.14 

6  14.99 

7.15 

6    7.83 

7.16 

6     0.07 

7.17 

98 

1     5  17.50 

7.22 

5  10.28 

7.23 

5    3.05 

7.24 

4  55.80 

7.24 

4  48.56 

7.25 

99 

I     4    4.89 

7.30 

3  57.59 

7.31 

3  50.28 

7.32 

3  42.96 

7.33 

3  35.63 

7.33 

100 

1     2  51.51 

7.38 

2  44.13 

7.38 

2  30.71 

7.39 

2  29.35 

7.40 

2  21.94 

7.40 

101 

1     1  37.39 

7.45 

1  29.95 

7.45 

1  22.49 

7.46 

1   15.03 

7.46 

1    7.56 

7.47 

102 

0  60  22.02 

7.51 

00  15.11 

7.51 

00    7.59 

7.52 

60    0.00 

7.53 

59  52.53 

7.53 

103 

0  59    7.23 

7.57 

58  59.00 

7.07 

58  52.08 

7.58 

58  44.50 

7.58 

58  36.91 

7.59 

104 

0  57  51.29 

7.62 

57  43.07 

7.62 

57  30.04 

7.63 

57  28.41 

7.63 

57  20.77 

7.64 

105 

0  50  34.80 

7.67 

50  27.19 

7.67 

56  19.52 

7.67 

50  11.84 

7.68 

56    4.16 

7.68 

106 

0  55  17.99 

7.71 

55  10.28 

7.71 

55    2.56 

7.71 

54  51.85 

7.73 

54  47.13 

7.72 

107 

0  54    0.74 

7.74 

53  53.00 

7.74 

53  45.25 

7.75 

53  37.50 

7.75 

53  29.75 

7.75 

108 

0  52  43.18  .. 

7.77 

52  35.40 

7.77 

52  27.63 

7*77 

52  19.85 

7.78 

52  12.07 

7.78 

109 

0  51  25.35 

7.79 

-    51  17.50 

7.79 

51     9.70 

7.80 

51     1.90 

7.80 

50  54.16 

7.80 

110 

0  50    7.33 

7.81 

49  59.52 

7.81 

49  51.71 

7.81 

49  43.89 

7.81 

49  36.08 

7.82 

111 

0  48  49.17 

-7.82 

48  41.34 

-7.82 

48  33.52 

-7.82 

48  25.70 

-7.82 

48  17.87 

-7.82 

TARIFF   X. 


K(,H    VHON  OF  TIIK  (TATIiK.  Foil  ill  =0. 

r..ii,.fmt  :nlil.-ii   17'  ::'•:..    ivn..,l  •»  •.'•.'  i  : 

d 

Dili'. 

.1 

Diff. 

,1 

Dill'. 

d 

Diir. 

d 

Diff. 

Arg  1             «)..-> 

tnrlM.I 

o.e 

fbrO    l 

0.7 

o.s 

fiirli'M 

<).!) 

lurlH.l 

1 

56 

0            /            // 

::i    (U)7 

ft 
-<i.M 

31    5'>> 

n 

-0.16 

31 

n 

31 

n 
-Ml 

:«(    5-u 

II 
-4M 

57 

:tl    3.5s 

:il    3.21 

• 

3  1     •'.-  1 

0.40 

31      •>.!() 

(1.1:1 

31      I.JKi 

IP.  i:. 

56 

33  ' 

33  5S.29 

0.60 

:{.-(  57.68 

:tt  57.CI 

:{-•(  50.3S 

SB 

:!-•(  51.  '.19 

o.H> 

33  51.  is 

:u  50.31 

».-  1 

.'ft  49.49 

:ct  is.oi 

00 

:»  42.90 

:t»  II.-; 

l.lll 

33    10.S-> 

1.06 

:«  :«i.7."> 

\M 

:KI  3s.t;o 

1.10 

01 

:{3  31.03 

\M 

33  3(t.:«» 

i.-.i; 

33  ->!M-.' 

\M 

:tt  -J7.-3 

:ti  20.52 

IJ» 

02 

33  is.2ti 

1  .  i."> 

:{••{  10.73 

1.47 

:t«  !5.-.>5 

i.n 

:«  13.71 

:i3  i  -.'.•>-.' 

I...I 

63 

:n    2.00 

It)    (i.!f» 

3-.'  S 

i  /.  i 

::.»  57.50 

i.;.i 

32  55.70 

1.78 

01 

:«  ll.s:; 

1.88 

3-J   !-.>.!  "7 

1.90 

:w  41.05 

1.99 

32  39.12 

l.:u 

32  37.17 

isn 

05 

:«  21.99 

:«  9 

Ul 

3-i  ->0.70 

•J.ll 

32   IS.OI 

32   10.15 

06 

32 

2.30 

:!-.'    o.i!» 

tM 

31   5S.35 

31   50.00 

31   53.02 

(17 

:il  3s/>2 

;n  3i;.in 

31   :',:{>;; 

2.55 

31   31.29 

31   21.71 

31    K'.77 

31    HUH 

a.74 

31     -.-*> 

2.76 

31     4.52 

' 

31      1.73 

2.80 

69 

30  41.50 

30    ll.ltt 

•J.'.ll 

30  3S.07 

tM 

30  35.70 

30  32.7  1 

3.00 

70 

30  14.32 

Ul 

30   11.1!) 

:i.n 

30    s.o:» 

3.16 

30     4  .SO 

3.18 

30      1.00 

3.90 

71 

29  12.(.- 

:).:« 

-.71 

:t.:u 

2!t  35.:J!i 

3.3G 

29  32.1.2 

29  2S.03 

3.40 

7'.' 

29 

:t..v_> 

2!)    4.:n 

3..-1  1 

99    0.7S 

Ul 

28  57.21 

3M 

53.69 

3.IM 

7:t 

2S  31.IM 

3.71 

•>•  -.•;.!  10 

3.73 

98  -i\.-f> 

S.7B 

•>   20.10 

3.77 

28    1  O.I  IS 

71 

•.'7  53.59 

3.90 

•>:  4!  1.07 

•A.-.i-l 

27  45.7  t 

3.UI 

-.'7  41.79 

Ul 

27  37.^2 

3.98 

75 

-.'7  13.00 

4.09 

27    !>..".() 

4.11 

27     5.3- 

4.13 

27     l.-.'l 

tM 

•JO  57.08 

4.17 

7(i 

20  31.75 

4.98 

2fi  27.  17 

4.99 

2fi  2:1.10 

4.31 

20   l-.-l 

4.33 

-.'0    11.50 

4..15 

77 

25 

4.46 

-.'.-.  43.0-.' 

4.47 

-.'5  3!M3 

4.19 

25  3l.li3 

•i.:.l 

25  30.11 

4.rk) 

78 

•r>   2.02 

4.63 

•21   57.!  is 

4.65 

24  Si.3l 

4.67 

24  4.-.01 

4.fi9 

•-'I   43.91 

4.70 

re 

21  15.40 

4.81 

24  10.58 

4.83 

24    5.75 

4.84 

24    0.90 

4.86 

23  5(5.03 

4.88 

HO 

23  20.10 

4.98 

23  21.  is 

4.99 

23  10.17 

5.01 

23  11.15 

5.03 

23     0.12 

tM 

81 

22  35.S5 

5.14 

•>•>  30.70 

5.16 

-,"2  -.'5.5.3 

5.18 

22  20.31 

5.19 

22   15.11 

:..•!  1 

83 

21  43.5H 

Ul 

•>(  a&aa 

:..:;.' 

21  :W.!I5 

tM 

21  27.00 

Ul 

21   22/.'  1 

5J7 

ta 

•JO  4!i.7l 

5.17 

•.M   !l/>7 

5.48 

20  3S.7- 

5.50 

20  33.-.'s 

5.51 

20  27.70 

5Ji3 

i-l 

19  5l.:t3 

5.G1 

10  4,-.7  1 

5.63 

19  43.07 

5.64 

19  37.41 

5.66 

19  31.74 

5.n7 

85 

is  57.11 

S.77 

18  51.03 

5.78 

IS    15.S5 

5.80 

18  40.04 

5.81 

18  34.23 

5.H-2 

86 

1    17  59.02 

5.91 

17  SI.  10 

5.93 

17  47.17 

5.94 

17  41.22 

5.95 

17  35.20 

5.97 

87 

1  10  r>:i.-.>0 

6.06 

1(5  53.15 

6.06 

16  47.07 

6.08 

16  40.99 

6.09 

10  34.8!) 

6.10 

ss 

i  15  saoi 

6.19 

15  51.82 

6.00 

15  45.62 

6.21 

15  39.40 

6.23 

15  33.10 

6.24 

BO 

1    11  55.50 

6.-.1-1 

14  4!i.l7 

6.33 

14  42.SI 

6.34 

14  30.19 

6.35 

14  30.13 

6«T7 

!K) 

1   13  51.70 

6.44 

13  4.V>5 

6.45 

13  3S.7!i 

6.46 

13  32.31 

6.48 

13  25.S3 

6.49 

!>1. 

1    12  40.00 

6.J6 

12  40.10 

6J7 

12  33.52 

6.:>9 

12  20.92 

6.60 

12  20.32 

6X1 

09 

1  11  40.15 

6.68 

11  33.77 

6.69 

11  27.07 

6.70 

11  20.37 

6.71 

11  13.05 

6.79 

98 

1  10  33.11 

6.79 

10  20.3-2 

6.80 

10  19.51 

6.82 

10  12.70 

6.83 

10     5.-7 

6.84 

M 

i    9  21.09 

6.89 

!»   17.7H 

6.90 

9  10.88 

6.91 

9     3.97 

6.99 

-  57.04 

6.93 

05 

1     8  15.25 

6.99 

8     8.25 

7.00 

8     1.21 

7.01 

7  54.22 

7.02 

7  47.19 

7.03 

96 

1     7    4.83 

7.09 

0  57.71 

7.10 

0  50.01 

7.11 

0    13.52 

7.13 

0  30.40 

7.19 

!I7 

1     5  53.50 

7.18 

5  40.31 

7.19 

5  39.1--' 

7.19 

5  31.93 

7.20 

5  24.72 

JM 

96 

1     4  41.30 

7.26 

4  3I.(,3 

7.27 

4  20.70 

7.28 

4   19.IS 

7.29 

4  12.19 

7.29 

'M 

1     3  28.30 

7.34 

3  20.1  »5 

7.33 

3  13.00 

7.3J 

3    0.24 

7.36 

2  58.88 

7.37 

100 

1     2  14.51 

7.41 

2    7.12  • 

7.42 

1  59.70 

7.42 

1   52.'.'7 

7.43 

1  44.84 

7.44 

101 

1     1     0.01) 

7.48 

0  52.150 

7.48 

0  45.12 

7.49 

0  37.02 

7.50 

0  30.12 

7JO 

102 

0  50  4  !.!>!> 

7..M 

5!l  37.15 

7.54 

59  29.91 

7..V» 

.V.i  22.35 

7.56 

59  14.79 

7J6 

103 

0  58 

7.59 

.58  21.73 

7.60 

58  14.12 

7.60 

58    6.52 

7.61 

57  58.91 

7.61 

101 

0  57  13.13 

7.01 

57    5.49 

7.65 

50  57^3 

7.65 

50  50.18 

7.66 

50  •]•>.:,•> 

7.66 

lor. 

0  55  50.47 

7.69 

55*  48.78 

7.69 

55  41.09 

7.69 

55  33.39 

7.70 

55  25.09 

7.70 

106 

0  51  39.41 

-.;•> 

51  31.  (X 

7.73 

51   '.'3.95 

7.73 

51   10.22 

7.73 

54    H.is 

7.71 

107 

0  53  21.99 

7.76 

53  14.23 

7.76 

53     0.17 

7.76 

52  58.71 

7.76 

52  50.94 

7.77 

H  - 

0  52    4.2!) 

7.78 

51   50.51 

7.78 

51  4S.7-.' 

7.79 

51  40.93 

7.79 

51  33.11 

7.79 

lOit 

0  r>()   |(i.:!ii 

7.80 

50  .'K50 

7.80 

50  30.75 

7.81 

50  2--'.!  "5 

50  15.14 

•,.-1 

110 

ii  19  -.'s.-jo 

7.89 

49  20.45 

7.89 

49  12.03 

7.89 

19     l.sl 

7.89 

48  5'i.99 

7.W 

111 

0  48  10.05       -7.83 

48    2.21 

-7.8S 

47  54.40 

-7.83 

47  46.57 

-7.83 

47  3S.75 

--..•:! 

TABLE    X. 


EQUATION  OF  THE  CENTRE,  FOR  in  =  0. 
Const;,  nt  ud.ln!  .17'  3".5.    Period  =  224.7008. 

Arg.  1. 

d 
O.O 

Ditr. 

for  (Kl 

d 

O.I 

Diff. 

for  OJ.l 

d 

O.i2 

Diir. 

forlKl 

(i 

0.3 

Diir. 

forOJ.l 

d 
O.4 

Diff. 
for  (K  1 

112 

61          II 
47  30.!>2 

ii 
-7.83 

/      // 
47  23.10 

ii 
-7.83 

/         // 

47  15.27 

II 
-7.83 

47     7V14 

ii 
-7.83 

40  5I.M32 

ii 
-7.83 

li:5 

0  46  12.66 

7.S2 

46    4.a3 

7.83 

45  57.01 

7.82 

45  49.19 

7.82 

45  41.36 

7.88 

114 

0  44  54.43 

7.89 

4!  46.61 

7.82 

44  38.80 

7.83 

44  30.98 

7.81 

44  23.17 

7.81 

115 

0  43  36.31 

7.81 

43  28.50 

7.80 

43  20.70 

7.80 

43  12.90 

7.80 

43    5.10 

7.80 

in; 

0  42  18.34 

7.79 

42  10.55 

7.78 

42    2.77 

7.78 

41  54.99 

7.78 

41  47.21 

7.78 

117 

0  41     0.5!) 

7.70 

40  52.82 

7.76 

40  45.07 

7.76 

40  37.31 

7.75 

40  29.56 

7.75 

118 

0  39  43.1  1 

7.73 

39  35.38 

7.73 

39  27.05 

7.72 

39  19.93 

7.72 

39  12.21 

7.72 

1H> 

0  38  25.97 

7.09 

38  18.28 

7.09 

38  10.59 

7.69 

38     2.90 

7.08 

37  55.22 

7.68 

120 

0  37    9.23 

7.C5 

37     1.58 

7.C5 

30  53.93 

7.64 

36  40.29 

7.04 

36  38.65 

7.63 

121 

0  35  52.93 

7.00 

35  45.33 

7.00 

35  37.74 

7.59 

35  30.14 

7.59 

35  22.56 

7.58 

139 

0  34  37.15 

7.55 

34  29.01 

7.54 

34  22.06 

7.54 

34  14.53 

7.53 

34     7.00 

7.53 

123 

0  33  21.91 

7.49 

33  14.46 

7.48 

33    6.97 

7.48 

32  59.50 

7.17 

32  52.03 

7.46 

1-24 

0  32    7.36 

7.42 

31  59.94 

7.42 

31  52.52 

7.41 

31  45.12 

7.40 

31  37.71 

7.40 

12.-) 

0  30  53.46 

7.33 

30  46.11 

7.35 

30  38.77 

7.34 

30  31,13 

7.33 

30  24.1  1 

7.32 

1% 

0  29  40.30 

7.98 

29  33.03 

7.27 

2!)  25.76 

7.26 

29  18.51 

7.25 

29  11.26 

7.24 

127 

0  28  27.94 

7.19 

28  20.75 

7.19 

28  13.57 

7.18 

28    6.39 

7.17 

27  59.23 

7.16 

128 

0  27  16.43 

7.11 

27    9.32 

7.10 

27    2.23 

7.09 

26  55.15 

7.08 

26  48.07 

7.07 

12!) 

0  26    5.82 

•7.01 

25  58.81 

7.00 

25  51.81 

6.99 

25  44.83 

6.98 

25  37.85 

6.97 

130 

0  24  56.18 

0.91 

24  49.27 

0.90 

24  42.37 

6,89 

24  35.48 

6.88 

24  28.60 

6.87 

131 

0  23  47.55 

6.81 

23  40.75 

6.80 

23  33.95 

6.79 

23  27.17 

0.78 

23  20.39 

0.77 

i:32 

0  22  39.99 

6.70 

22  33.29 

0.09 

22  26.61 

6.68 

22  19.94 

0.67 

22  13.27 

0.06 

133 

0  21  33.55 

6.59 

21  26.97 

0.57 

21  20.40 

6.56 

21  13.64 

6.55 

21     7.30 

0.54 

134 

0  20  28.28 

6.47 

20  21.82 

6.43 

20  15.37 

6.44 

20     8.93 

6.43 

20    2.51 

6.42 

135 

0  19  24.23 

6.34 

19  17.8!) 

6.33 

19  11.57 

6.32 

19    5.26 

6.30 

18  58,96 

6.29 

136 

0  18  21.45 

6.31 

18  15.24 

6.20 

18    9.05 

6.19 

18    2.87 

6.17 

17  50.70 

6.16 

137 

0  17  19.99 

6.08 

17  13.92 

0.00 

17     7.86 

6.05 

17     1.82 

6.04 

16  55.79 

6.113 

1138 

0  16  19.90 

5.94 

16  13.96 

5.92 

16    8.05 

5.91 

16    2.14 

5.90 

15  56.25 

5.88 

13'J 

0  15  21.22 

5.80 

15  15.43 

5.78 

15    9.06 

5.77 

15    3.90 

5.75 

14  58.15 

5.74 

140 

0  14  24.00 

"i.lj.") 

14  18.36 

5.03 

14  12.73 

5.62 

14     7.12 

C.61 

14     1.53 

5.59 

141 

0  13  28.28 

5.49 

13  22.79 

5.48 

13  17.32 

5.40 

13  11.87 

5.45 

13    6.43 

5.43 

112 

0  12  34.12 

5.34 

12  28.79 

5.32 

12  23.17 

5.31 

12  18.17 

5.29 

12  12.89 

5.27 

143 

0  11  41.54 

5.18 

11  36.37 

5.17 

11  31.22 

5.15 

11  26.08 

5.13 

11.20.96 

5.11 

144 

0  10  50.59 

5.01 

10  45.59 

5.00 

10  40.60 

4.98 

10  35.03 

4.96 

10  30.68 

4.94 

145 

0  10     1.32 

4.84 

9  56.48 

4.83 

9  51.00 

4.81 

9  46.86 

4.79 

9  42.08 

4.77 

140 

0    !)  13.75 

4.67 

9    9.09 

4.  65 

!)    4.45 

4.03 

8  59.82 

4.62 

8  55.21 

4.60 

147 

0    8  27.  3 

4.49 

8  23.45 

4.47 

8  18.98 

4.46 

8  14.54 

4.44 

8  10.11 

4.42 

148 

0    7  43.90 

4.31 

7  39.00 

4.29 

7  35.31 

4.28 

7  31.04 

4.26 

7  26.80 

4.24 

14!) 

0    7     1.69 

4.13 

0  57.57 

4.11 

6  53.17 

4.09 

6  49.38 

4.07 

6  45.32 

4.05 

150 

0    6  21.33 

3.94 

0  17.39 

3.92 

6  13.48 

3.90 

6    9.59 

3.89 

6    5.71 

3.87 

151 

0    5  42.85 

3.75 

5  39.11 

3.73 

5  35.38 

3.71 

5  31.68 

3.69 

5  28.00 

3.03 

152 

0    5    6.29 

3.56 

5    2,74 

3.54 

4  59.21 

3.53 

4  55.70 

3.50 

4  52.21 

3.48 

153 

0    4  31.08 

3.30 

4  28.32 

3.34 

4  24.99 

3.32 

4  21.  68 

3.30 

4  18.38 

:u'8 

154 

0    3  59.04 

3.16 

3  55.88 

3.14 

3  52.75 

3.13 

3  4!  MM 

3.10 

3  46.54 

3.08 

155 

0    3  28.40 

2.96 

3  25.44 

2.94 

3  22.51 

2.98 

3  19.60 

2.90 

3  10.70 

2.b8 

156 

0    2  59.78 

8.78 

2  57.03 

2.74 

2  54.30 

2.73. 

2  51.59 

2.70 

2  48.90 

2.08 

157 

0    2  33.21 

2.55 

2  30.67 

2.53 

2  28.14 

2.51 

2  25.64 

2.49 

2  23.10 

2.47 

158 

0    2    8.71 

2.35 

2    6.38 

2.32 

2    4.06 

2.30 

2     1.77 

2.28 

1  59.50 

2.26 

159 

0     1  46.31 

2.13 

1  44.18 

2.11 

1  42.08 

2.09 

1  40.00 

2.07 

1  37.94 

2.05 

160 

0     1  26.01 

1.93 

1  21.10 

1.90 

1  22.21 

1.88 

1  20.34 

1.86 

1   18,19 

1.84 

161 

0     1     7.84 

1.71 

1     0.14 

1.69 

1     4.47 

1.67 

1     2.81 

1.05 

1     1.17 

1.62 

102 

0    0  51.81 

1.49 

0  50.33 

1.47 

0  48.87 

1.45 

0  47.43 

1.43 

0  46,01 

1.41 

163 

0    0  37.94 

J.28 

0  36.68 

1.26 

0  35.43 

1.23 

0  34.21 

1.21 

0  33.00 

1.19 

164 

0    0  26.24 

i.no 

0  25.19 

1.04 

0  24.16 

1.03 

0  23.10 

1.00 

0  22.17 

0.97 

165 

0    0  16.72 

0.84 

0  15.89 

0.83 

0  15.08 

0.80 

0  14.29 

0.78 

0  13.53 

0.76 

100 

0    0    9.39 

0.03 

0     8.77 

0.00 

0    8.18 

0.58 

0     7.01 

0.56 

0    7.07 

0.54 

167 

0    0    4.25 

-11.10 

0    3.86 

-0.38 

0    3.49 

-0.36 

0    3,14 

-0.34 

0    2.81 

-0.32 

TABLE    X. 


FETATION  (IK  TIIK  (T.NTlii:,  F<  >U  III  =  0. 

Coiislant  add.-il   -17'  T'.5.      IVriml  =  22  1  : 

d 

Diff. 

,1 

Diff. 

.1 

Diff. 

d 

.1 

Diff. 

()..-, 

CorO*.l 

O.6 

0.7 

O.S 

lurlH.I 

().:) 

,1 

119 

o       /       /; 
0  40  51.79 

-7.83 

lii  4:i!!Hi 

40  30.'  1  1 

-7.*! 

/       // 
lii  2S.3I 

lii  20.'  19 

113 

0  45  :t».54 

45  25.72 

45   17.90 

45   10.07 

45     2.25 

111 

Oil   15.:  {5 

1  1     7.5  1 

43  5!  1.73 

7.-I 

13  51.92 

:.-\ 

43   11.11 

7.  s| 

115 

0  42  57.30 

42   19.50 

12  41.71 

12  :!3.92 

42  20.13 

7.7'J 

110 

0  41  39.13 

7.77 

II   31.00 

7.77 

41  2. 

-  "7 

41    10.12 

1  1     s.:J5 

7.76 

117 

0  40  2I.M 

7.7:. 

40   11.00 

7.71 

40     0.32 

7.71 

:t:i  5S.58 

7.71 

:?»  -•  -I 

7.71 

us 

0  39      1.50 

7.71 

3"  50.7S 

7.71 

3s    : 

7.71 

11.37 

7.7U 

:;8  :t;..  ,7 

7.70 

119 

0  37   17.55 

7.li7 

37  :i9,-7 

7.67 

37  32.21 

37  01.51 

37  Ji>.88 

7.CJ 

120 

0  30  31.02 

3  i  23.39 

30  15.77 

30     8.15 

7.11. 

30    0.51 

7.  lii 

121 

0  35   11.9," 

35     7.10 

31  59,-! 

7.57 

31  52.27 

31  41.;  1 

199 

0  :«  59.47 

:Ci  51.  'Hi 

7..M 

33  41.11 

",  .  .  ,  1 

.33  30.91 

33  29.  !  1 

123 

0  32   1  1.57 

7.  Ill 

32  37.11 

7,1.-, 

32  29.07 

7.  i;, 

32 

7.11 

32   14.79 

7.IJ 

121 

0  31  30.32 

7.39 

31   22.!  i| 

31    15.50 

7.38 

31      8.18 

7_'I7 

31     0.8-7 

7.36 

125 

0  30    10.79 

Ml 

30     9.17 

7.;:i 

30     2.17 

7.30 

99  5I,"7 

2:l  47.58 

IM 

120 

0  29      1.02 

7.-J1 

2-  50.7," 

7.  Ml 

2"    19.50 

7.  •_'•.! 

2-    12.31 

7.-.M 

15.14 

IM 

127 

0  27  52.07 

7.15 

27  44.92 

7.11 

27  37.79 

7.13 

27  30.00 

7.1- 

27  23.51 

7.13 

HB 

0  20  41.01 

7.C6 

2i  i  33.!  15 

26  26.91 

7.04 

26  19X7 

7  .11.1 

20  12.  -I 

7.02 

199 

o  25  :tn.,"s 

6.96 

25  23.!  12 

tM 

25   10.97 

6.94 

25  10.03 

6.93 

25     3.10 

130 

021  21.73 

6.86 

24   II,— 

i;.-:, 

21     8.03 

6.84 

21     1.19 

6.83 

23  51.37 

6.SJ 

131 

0  23   13.03 

6.76 

23     0.,-s 

C.73 

23     0.14 

6.73 

22  53.11 

G.72 

22    10.09 

C.71 

132 

0  22    0.02 

6.64 

21   5!  P.!  19 

6.63 

21  53.30 

21  40.71 

6.61 

21  40.14 

6.60 

133 

0  21     0.70 

&:,:i 

20  51.21 

li..M 

20  47.73 

6.50 

20  41.21 

6.19 

20  31.75 

134 

0   19  50.10 

6.40 

19  49.70 

6.39 

19  43.31 

6.38 

19  30.91 

6.37 

19  30.58 

li.X, 

135 

0  18  52.08 

6.28 

18  40,10 

6.37 

18  40.14 

6.35 

18  33.!>0 

6.24 

18  27.(,7 

6.93 

136 

0  17  50.55 

6.15 

17  44.11 

6.13 

17  38.28 

6.13 

17  .32.17 

6.11 

17  20.07 

tM 

137 

0    10    19.77 

6.01 

10  43.77 

Hi  37.78 

5.98 

10  31.80 

5.97 

16  25,-  1 

5.95 

138 

0  15  50.3," 

5.87 

15   11.52 

5.89 

15  38.07 

5.84 

15  32,"  1 

5.83 

15  27.02 

'5.M1 

130 

0  14  52.12 

5.73 

14  40.71 

5.71 

1  1  41.01 

5.69 

14  35.32 

5.68 

14  29.65 

5.66 

140 

0  13  55.95 

tM 

13  50.38 

13  ll.sl 

5.54 

13  39.30 

5.13 

13  33.78 

5.51 

111 

0  13     1.00 

.'i.  !•> 

12  55.5!  1 

5.40 

12  50.20 

5.38 

12   1  1,"2 

5.37 

12  39.10 

5-'G 

142 

0  12     7.03 

5.96 

12    2.:t8 

:,.•_'  I 

11  57.14 

5.33 

11  51.92 

5.21 

II   40.72 

5.19 

143 

0  11   15.,"0 

5.09 

11  10.77 

5.08 

1  1     5.70 

5.06 

11     0.05 

5.04 

10  55.01 

5.03 

144 

0  10  25.74 

4.93 

10  20.82 

4.91 

10  15.92 

4.89 

10  11.04 

4.88 

10    6.17 

4.86 

145 

0    9  37.32 

4.76 

9  32.57 

4.74 

9  27.,"  1 

4.72 

9  23.12 

4.70 

9  18.43 

4.69 

110 

0    8  50.02 

4.58 

8  40.05 

4.56 

8  41.49 

4.M 

8  30.96 

4_M 

8  32.  1  1 

4.51 

147 

0    8    5.69 

4.40 

8     1.30 

4.39 

7  56.92 

4.37 

7  52.56 

4.35 

7  48.22 

4J3 

148 

0    7  22.56 

4.32 

7  18.35 

4.90 

7  14.10 

4.18 

7     9.9," 

4.17 

7    5.83 

I.I.-. 

149 

0    6  41.27 

l.lll 

0  37.25 

4.<h> 

0  33.24 

4.00 

6  29.25 

3.98 

6  25.2" 

3.9S 

150 

0     6      1.85 

3.85 

5  58.01 

3.83 

5  54.20 

3.81 

5  50.40 

3.79 

5    10.01 

3.77 

151 

0    5  24.33 

3.66 

5  20.08 

3.C4 

5  17.06 

3.62 

5  13.45 

3.60 

5    9.SO 

3.58 

152 

0    4  4s.7  1 

3.46 

1    15.29 

:i.n 

4  41>5 

:i.  i-j 

4  38.  1  1 

3.40 

4  a>.o.-> 

X18 

153 

0    4  15.11 

3.26 

1   11.,"5 

tM 

4     8.02 

3.23 

4     5.41 

3.30 

4     2.21 

:t.iH 

154 

0    3  43.46 

3.06 

3  40.11 

3.04 

3  37.38 

3.02 

3  31.37 

3.00 

3  31.37 

3J8 

155 

0    3  13.83 

2.86 

3  10.98 

2.84 

3    8.15 

2.82 

3     5.31 

2.80 

3    2.55 

2.78 

156 

0    2  40.21 

2.66 

2  43.59 

2.64 

2  40.97 

2.69 

2  .38.30 

2.59 

2  35.78 

9i7 

157 

0    2  20.70 

2.45 

2  18.20 

2.43 

2  15.H1 

2.41 

2  13.15 

2.39 

2  11.07 

2J7 

158 

0     1  57.25 

2.-J  1 

1  55.02 

tM 

1   52.82 

3.20 

1  50.02 

9.18 

1    I".I5 

2.16 

159 

0     1  35.!  »0 

2.03 

1  33.88 

2.01 

1  31.88 

1.99 

1  29.90 

1.97 

1  27.95 

1.94 

160 

0     1    10.00 

1.82 

1  14.&5 

1.80 

1    13.07 

1.77 

1  11.30 

1.7.-, 

1     9.50 

1.73 

161 

0     0  59.5i  i 

1.60 

0  57.!  >7 

1.58 

0  50,10 

1.56 

0  54,  "5 

1.54 

0  53.32 

1.59 

162 

0    0  41.01 

1.39 

0  43.23 

IJ7 

0  41.-- 

IM 

0  40.51 

IM 

0  3.>.23 

IM 

ni3 

0    0  31.82 

1.17 

0  30.00 

1.15 

0  29.53 

1.13 

0  28.41 

1.10. 

0  27.32 

IMS 

101 

0    0  21.21 

0.95 

0  20.27 

0.93 

0  19.35 

0.91 

0   18.15 

0.89 

0  17.57 

0.86 

165 

0    0  12.78 

0.73 

0  12.00 

0.71 

0  11.30 

0.09 

0   10..  i" 

ojtn 

0  10.02 

tM 

[66 

0    0    0.51 

0.-)I 

0    6.01 

0.49 

0    5.50 

0.47 

0     5.10 

tM 

0    4.00 

0.43 

107 

0    0    2.51 

-0.39 

0    2.22 

-0.37 

0    1.90 

-0.35 

0     1.73 

-OJO 

0     1.51       -0.91 

TABLE    X. 


EQUATION  OF  THE  CENTRE,  FOR  111  =  0. 

d 

Constant  suUK-il  47'  :{».o.     Period  =  224.  7008. 

Arg.  L. 

d 

o.o 

Diff. 

forO'l.l 

cl 

0.1 

DilK. 

lor  [)'".! 

<1 

0.2 

Diff. 

for  (><U 

(1 

0.3 

DifT. 

for  (!'".! 

d 
O.4 

Did'. 
forO"i.l 

d 

o       i       n 

it 

/          // 

II 

1         11 

n 

/       // 

ii 

/            // 

u 

168 

0     0     1.31 

-0.18 

0     1.14 

-0.16 

0     0.99 

-0.14 

0     0.8!  i 

-0.12 

0    0.70 

-0.10 

Ifi9 

0     0     0.58 

+0.04 

0    0.03 

+0.06 

0    0.70 

+0.08 

0    0.79 

+0.10 

0    0.91 

+0.13 

170 

0    0    2.0(5 

0.26 

o    2.33 

0.28 

0    2.62 

0.30 

0    2.93 

0.39 

0    3.27 

'  0.35 

171 

0    0    5.74 

0.43 

0    6.23 

0.50 

0    0.75 

0.52 

0    7.28 

0.54 

0    7.84 

0.57 

17-3 

0    0  11.  (54 

0.70 

0  12.35 

0.72 

0  13.08 

0.74 

0  13.83 

0.76 

0  14.01 

0.79 

17:! 

0    0  19.73 

0.92 

0  20.06 

0.94 

0  21.01 

0.96 

0  22.59 

0.98 

0  23.58 

1.01 

171 

0    0  .'!0.02 

1.14 

0  31.17 

1.10 

0  32.34 

1.18 

0  33.54 

1.20 

0  34.75 

1.22 

175 

0    0  42.5  1 

1.:16 

0  43.88 

1.38 

0  45.27 

1.40 

0  40.08 

1.42 

0  48.11 

1.44 

17(5 

0    0  57.18 

1.58 

0  58.76 

1.60 

1     0.37 

1.62 

0    2.00 

1.64 

0    3.05 

1.66 

177 

0     1   14.02 

1.79 

1  15.82 

1.81 

1    17.05 

1.K4 

1   19.50 

1.86 

1  21.30 

1.88 

178 

0     1  33.03 

a.oi 

1  35.04 

2.03 

1  37.08 

9.05 

1  3!).  15 

2.07 

1  41.23 

2.09 

179 

0     1  54.18 

2.22 

1  50.41 

2.24 

1  58.07 

9.26 

2    0.94 

2.29 

2    3.24 

2.31 

180 

0    2  17.47 

2.43 

2  19.91 

2.46 

2  22.38 

2.48 

2  24.87 

2.50 

2  27.38 

9.52 

181 

0    2  42.87 

8.05 

2  45.53 

2.07 

2  48.20 

9.09 

2  50.!  >0 

2.71 

2  53.02 

2.73 

18'2 

0    3  10.37 

2.85 

3  13.24 

2.87 

3  16.12 

2.90 

3  19.03 

2.92 

3  21.90 

8.94 

183 

0    3  39.95 

3.0G 

3  43.02 

3.08 

3  46.12 

3.10 

3  49.23 

3.12 

3  52.30 

3.14 

184 

0    4  11.59 

3.27 

4  14.87 

3.29 

4  18.16 

3.31 

4  21.48 

3.33 

4  24.82 

3.35 

189 

0    4  45.2(5 

3.47 

4  48.74 

3.49 

4  52.23 

3.51 

4  55.75 

:i.r,:i 

4  59.29 

3.55 

181) 

0    5  20.93 

3.07 

5  24.01 

3.69 

5  28.31 

3.71 

5  32.02 

3.73 

5  35.70 

3.75 

187 

0    5  58.59 

3.86 

6    2.46 

3.88 

(5    0.36 

3.90 

6  10.27 

3.92 

0  14.20 

3.94 

188 

0    6  38.20 

4.06 

6  42.26 

4.08 

6  40.35 

4.10 

0  50.46 

4.11 

6  54.58 

4.13 

189 

0    7  19.73 

4.25 

7  23.98 

4.27 

7  28.26 

4.29 

7  32.55 

4.30 

7  3(5.87 

4.32 

1!IO 

0    8    3.14 

4.43 

8    7.59 

4.45 

8  12.05 

4.47 

8  10.53 

4.49 

8  21.03 

4.51 

191 

0    8  48.42 

4.C2 

8  53.05 

4.64 

8  57.0!) 

4.65 

9    2.36 

4.67 

9    7.04 

4.69 

199 

0  f9  35.51 

4.80 

9  40.32 

4.82 

9  45.15 

4.83 

9  49.99 

4.85 

9  54.85 

4.87 

199 

0  10  24.40 

4.98 

10  29.38 

4.99 

10  34.38 

5.01 

10  39.40 

5.03 

10  44.44 

5.01 

ID! 

0  11  15.02 

5.15 

11  20.18 

5.17 

11  25.35 

5.18 

11  30.55 

5.90 

11  35.75 

5.92 

1!>5 

0  12    7.313 

5.32 

12  12.68 

5.33 

12  18.03 

5.35 

12  23.39 

5.37 

12  28.7(5 

5.38 

196 

0  13     1.36 

5.48 

13    6.85 

5.50 

13  12.36 

5.51 

13  17.88 

5.53 

13  23.42 

5.55 

197 

0  13  5(5.!)!) 

5.04 

14    2.64 

5.66 

14     8.31 

5.67 

14  13.99 

5.69 

14  19.09 

5.71 

198 

0  14  54.20 

5.80 

15    0.01 

5.81 

15     5.a3 

5.83 

15  11.07 

5.84 

15  17.52 

5.86 

190 

0  15  52.95 

5.95 

15  58.91 

5.96 

10    4.88 

5.97 

16  10.87 

5.99 

16  16.87 

6.01 

200 

0  10  53.19 

6.10 

16  59.29 

C.ll 

17    5.41 

6.13 

17  11.54 

6.14 

17  17.69 

6.15 

301 

0  17  54.87 

6.84 

18     1.12 

6.25 

18     7.38 

6.27 

18  13.155 

6.28 

18  19.94 

6.89 

202 

0  18  57.95 

0.38 

19    4.*) 

6.39 

19  10.72 

6.40 

19  17.13 

6.42 

19  23.50 

6.43 

20:5 

0  20    2.37 

6.51 

20    8.88 

6.52 

20  15.41 

6.53 

20  21.95 

6.55 

20  28.50 

0.56 

204 

0  21     8.09 

6.03 

21  14.73 

6.65 

21  21.38 

0.00 

21  28.05 

6.07 

21  34.72 

6.68 

'205 

0  22  15.04 

6.7C 

22  21.81 

6.77 

22  28.58 

6.78 

22  35.37 

6.79 

22  42.10 

6.60 

906 

0  23  23.1!) 

6.87 

23  30.07 

6.88 

23  30.9(5 

6.89 

23  43.80 

6.91 

23  50.77 

6.92 

207 

0  24  32.48 

6.98 

24  39.47 

6.99 

24  46.40 

7.00 

24  53.47 

7.02 

25    0.50 

7.03 

208 

0  25  42.84 

7.09 

25  49.!  )3 

7.10 

25  57.04 

7.11 

26    4.15 

7.12 

2G  11.28 

7.13 

209 

0  2(5  54.23 

7.19 

27     1.42 

7.20 

27    8.62 

7.21 

27  15.84 

7.29 

27  23.00 

7.83 

210 

0  28     (5.5!) 

7.98 

28  13.87 

7.29 

28  21.17 

7.30 

28  28.47 

7.31 

28  35.79 

7.39 

211 

0  29  19.85 

7.37 

29  27.23 

7.38 

29  34.01 

7.39 

29  42.00 

7.40 

29  49.40 

7.40 

212 

0  30  33.!)7 

7.45 

30  41.43 

7.46 

30  48.89 

7.47 

30  56.30 

7.48 

31     3.84 

7.48 

213 

0  31  48.88 

7.5!) 

31  5(5.41 

7.54 

32    3.95 

7.54 

32  11.50 

7.55 

32  19.05 

7.56 

214 

0  33    4.52 

7.60 

33  12.13 

7.61 

33  19.74 

7.61 

33  27.35 

7.62 

33  34.!  )7 

7.63 

215 

0  34  20.84 

7.06 

34  28.51 

7.67 

34  36.18 

7.67 

34  43.86 

7.08 

34  51.54 

7.69 

2Hi 

0  35  .37.77 

7.72 

35  45.49 

7.73 

35  53.22 

7.73 

30    0.95 

7.74 

30    8.69 

7.74 

217 

0  3(5  55.24 

7.77 

37    3.02 

7.78 

37  10.80 

7.78 

37  18.58 

7.79 

37  20.37 

7.79 

218 

0  38  13.21 

7.82 

38  21.03 

7.82 

38  28.85 

7.83 

38  30.08 

7.83 

38  44.51 

7.83 

219 

0  39  31.00 

7.86 

39  39.46 

7.86 

39  47.32 

7.87 

39  55.19 

7.87 

40    3.00 

7.87 

220 

0  40  50.35 

7.89 

40  58.24 

7.89 

41    0.13 

7.90 

41  14.03 

7.90 

41  21.93 

7.90 

221 

0  42    9.10 

7.92 

42  17.32 

7.92 

42  25.24 

7.92 

42  .33.10 

7.92 

42  41.09 

7.93 

•••:•> 

0  43  28.158 

7.!)4 

43  30.02 

7.94 

43  41.50 

7.94 

43  52.51 

7.94 

44     0.45 

7.94 

an 

0  44  48.14 

TJH 

•II  50.10 

7.95 

45    4.05 

7.95 

45  12.00 

7.96 

45  19.90 

7.96 

•J2-1 

0  4(5    7.71 

+7.90 

46  15.07 

+7.96 

4(5  23.63 

+7.96 

40  31.59 

+7.96 

4(3  39.55 

+7.90 

TABLE    X. 


I:QI  ATION  OF  TIII-:  CKNTUK,  FOII  m=o. 

.! 

>           .:  ,uiii.-,i  IT'  :!".:>.    ivn.ui  -=  221  ; 

\rg  1 

d 
<)..-. 

Dill'. 
f.irO'U 

.1 
0.<i 

Diff. 

l.irlf'.l 

.1 

0.7 

Diff. 

.1 

O.8 

Diff. 

f.,ril'i.l 

d 
0.!> 

Diff. 

r.,r(l''.I 

,i 
Ki8 

0 

ti   (i   o.or 

n 

-<>.l>7 

d    (Mil 

// 

d    i 

ii 

1  1    1  1.:,:, 

// 
HM)I 

6  fa, 

II 

+<l.lll 

108 

0     0      1.05 

+0.19 

0      1.20 

M.n 

0     l.::s 

0      l.5!l 

0      I.SI 

I'.-.'l 

170 

0     0     :!.li:t 

0     1.01 

0     l.ll 

ii.n 

0      I.S3 

11.  I.I 

0     5/,'S 

M| 

171 

0    0     -.11 

(1   il.01 

n.hi 

0     !Mil 

0.63 

0    10.28 

o  lo.:  15 

048 

172 

0    0  15.11 

o  io.23 

o.si 

0  17.07 

ox. 

0  17.!  >3 

0    I,  -..-2 

n.!io 

17:! 

(1     0  21.00 

l.iti 

(1  25.01 

!.»:. 

28.70 

1.117 

0  27.711 

0  '.'- 

tM 

171 

0    0  35.!  i!  i 

0  37.25 

i  .•;; 

0  3S..VI 

0  3:».K{ 

l.:il 

o  II.  Hi 

l.::l 

17.-, 

(I     (I   1  '.:,7 

i.r, 

(1  51.05 

i.i'j 

0  52.55 

I..M 

0  51.07 

0  55.01 

tM 

170 

0     1     5.:t3 

IM 

1     7.02 

1.71 

1     S.7  1 

1.73 

1    10.  Is 

1    I".'.') 

U71 

177 

0     1   23.25 

1  25.|ii 

1  27.10 

IM 

1   2!  1.05 

1   3I.C3 

UK 

178 

0     1    13..33 

•J.  1  -J 

1    45.|ii 

•.'.i  i 

1    !7.';i 

L'.lli 

I   4H.78 

ua 

1   51.!  17 

3.30 

1711 

ii    •_>    5.50 

2    7.:  HI 

UB 

2    I0.2(i 

i:i7 

2   12.01 

•-'    15.01 

-Ml 

180 

(1     '.'  2!>.!  l| 

•J.:.  I 

2  32.  l(i 

2  35.0-3 

2  37.02 

2    Kl.-.'l 

|S| 

0    2  r>ii.:{ii 

2  5:i.l2 

•J.77 

3     l.!i| 

3     4.71 

3    7.r>:{ 

183 

o    :i  2i.:n 

3  27.S7 

3  30 

:i.oo 

3  :t.!.-; 

tM 

3  30.!  10 

:i.i>4 

183 

o   ;«  55.52 

3  SSJSS 

3.18 

1     1.88 

;i.-jii 

1      5.10 

tM 

1     s.:n 

181 

0     1 

:I.:IT 

1  31.55 

:i.:w 

•1  31.!  15 

:i.n 

1  3S.30 

Ml 

!.80 

.'!.  I.', 

185 

d   5     .  -, 

:i.:,r 

5     O.l> 

5  1 

5    13.01 

UK 

5   17.28 

:i.K, 

I    . 

d    r,  3.1.5.! 

3.77 

5    |:i.     i 

5   17.0!) 

n.-i 

5  50.!  KI 

5  51.71 

:i.  -I 

187 

d    d  is.15 

:i.:i(i 

(i  22.  U 

:i.9s 

ii  •:.;.!! 

4.00 

(i  :U12 

0  31.15 

-l.nl 

I  ;; 

0     (i 

i.i.i 

7  a. 

1.17 

7    7.'  , 

1.1!) 

7    11.27 

4.31 

7   15.1!) 

189 

o   7  -11.20 

r.:n 

7    15.55 

436 

7  4!t.!i2 

ua 

7   51.31 

4.40 

7  58.72 

I.I.' 

190 

0   8  25.55 

4J3 

s  30.09 

4.54 

s  :U.(it 

ut 

8  3:i.2l 

I..V- 

e  i3.8i 

\M 

191 

0    !>  11.71 

4.71 

i)  Ki.lii 

4.73 

it  21.20 

i.:  , 

!»  2.V.  15 

4.76 

!"  30.72 

4.78 

109 

0    !)  5!  i.73 

4.89 

10     4.03 

4.91 

10    !».."> 

4.IKJ 

10  14.48 

4.94 

10    I!U3 

4.96 

193 

0  10  4!>.l!) 

5.06 

10  51.57 

5.08 

10  5!Mi5 

5.10 

11     4.70 

ut 

11      9JBS 

IIM 

0  11  40.!)8 

ua 

II   4(i.22 

II   51.  IS 

5.27 

11  50.70 

5.2S 

12     2.05 

:,.:m 

195 

d  12  31.15 

5.40 

12  3 

:..  i  •• 

12  -1  >.!>!• 

5.43 

12  50.43         5.45 

12  S&89 

196 

0  1:1  2s.:  is 

13  31.55 

538 

13   10.13 

5.59 

13  45.74         :..6l 

13  51.30 

5^1 

197 

0  14  •-C-.K) 

11  31.13 

.-..-,  1 

1  1   3(i.8.-l 

:..;:, 

14  42.04         5.77 

1  1  48.4  1 

198 

0  15  2:  ».3:i 

15  2D.27 

5.89 

15  35.17 

5.90 

15  41.08 

5.93 

15  47.01 

\'M 

0  10  ' 

6.03 

10  2s.:  12 

6.04 

Ki  34.90 

6.05 

Ki  41.02 

6.07 

Ki  47.10 

Bjoa 

200 

0  I/  23.85 

6.17 

17  30.03 

6.18 

17  :j!i.22 

6.00 

17  42.42 

Mi 

17  is.iii 

301 

(1  IS  20.24 

•  6.31 

is  :!2.55 

i;.:w 

18  3S.-- 

6.33 

18  45.22 

ex- 

IS  51..,- 

202 

0  111  2!>.!>!) 

Ml 

III  30.11 

6.46 

l:i   12.!  H) 

6.47 

1'J  4!i.:tS 

6.48 

1!)  55,-7 

ii.  r.i 

203 

0  20  :15.07 

6.57 

20  41.  (15 

B.58 

20  is.-j| 

6.60 

20  54.84 

6.61 

21      1-10 

6.UJ 

304 

0  21  41.41 

6.70 

21  48.12 

6.71 

21  54.83 

6.72 

22    1.50 

6.73 

22     8.'J!» 

i;.;i 

205 

0  22  -IS.!  17 

ut 

22  55.71  > 

6.83 

23    2.<i3 

6.84 

23    -I.I7 

2:i  i  <;.:» 

6.«6 

20(5 

0  23  57.70 

IM 

21      1.03 

6.94 

21    11.57 

6.95 

24  18.53 

li.M 

21  25.511 

I-..1IT 

207 

0  25     7.53 

7.04 

25   14.57 

IM 

25  21.02 

7.06 

25  28.0!) 

7.07 

25  35.70 

|J 

7.0U 

208 

0  2f,  IS.  11 

7.14 

'.'li  25.55 

T.1S 

20  :i2.71 

7.16 

20  3!  1.87 

7.17 

2(i   17.05 

7.18 

20!) 

0  27  30.2:i 

IM 

27  37.53 

;.-.M 

27  44.78 

-..•£< 

27  52.01 

-,.-M 

27  5!  1.31 

2)0 

0  28  43.ll 

7J3 

28  50.44 

7J4 

28  57.7S 

7.34 

2!'     5.13 

IM 

2.)    12.1!) 

7.:«i 

211 

o  aa  5<;.8i 

7.11 

30    4.23 

7.ia 

30  11.G5 

7.43 

30  I'J.08 

7.44 

30  20.52 

-,.ll 

212 

0  31  11.33 

7.19 

31  18.83 

7^0 

31  20.33 

7..M 

31  33.84 

1AI 

31  41.30 

213 

0  32  20.01 

7.58 

32  31.  IS 

7.:>7 

32  41.70 

7^8 

32  4!».3J 

32  50.!  13 

^30 

"1  1 

o  33  I2.oo 

7.63 

:«  50.24 

7*1 

3.)  57.88 

7.64 

31     5.53 

7.65 

31    13.18 

7.G6 

215 

0  34  5!  i.23 

7.69 

35    (i.!l3 

7.70 

35  14.03 

7.70 

35  22.31 

7.71 

;r>  30.05 

7.71 

210 

0  3()  10.44 

7.75 

3(i  21.  lit 

7.r:> 

36  31.!  15 

7.76 

30  3!  ".71 

7.76 

::;  17.17 

7.77 

217 

0  37  31.17 

7.K) 

37  41.!  17 

7.80 

37   l!>.77 

7.81 

37  57.58         -.xi 

:..3!) 

7.81 

218 

0  38  52.35 

'..-I 

3't     O.lit 

7^4 

;«)    s.oi 

7.85 

311   15.811 

7.85 

80  23.71 

7^5 

21!) 

0  40  IO.H3 

40  is.-i 

7.88 

40  20.0.  > 

7.68 

40  34.57 

7.88 

40  42.10 

7.89 

220 

0  41  29.84 

7.01 

II  37.71 

7.91 

41  45.05         7.9i 

41  53.57 

7.91 

!•!      1.18 

7.93 

221 

0  42  4!'.02 

7.33 

42  5l  ;.!>5 

7.93 

43     1,-s 

7.93 

43   I2.-I 

7.93 

13  20.75 

KM 

222 

0    11      S.  10 

7.!>:> 

11   l(i.31 

7.95 

44  2l.2:i 

UB 

II  32.21 

7JB 

II    10.l!> 

223 

0    15  '.'7  .!>•> 

7.% 

-15  35.S7 

7.96 

15  4:!.S3 

7.96 

15  5  1.7!  >         7.!>6 

15  5H.75 

224 

0  4(5  47.52 

+7.S6 

4(i  55.18 

+7.W 

47    3.44       +7.96 

47  11.40     ;  +7.96         47  1 

+7.96 

TABLE  XI. 


TABLE  XII. 


Perturbations  «/'  the   Longitude. 

Factor  to  be  multiplied  l)y  the  integer  m  ;  and  its  Logarithm. 

Pert,  of  the  Long. 
Fact,  to  be  X  f.™)2 

*  LOU' 

Arg.I 

Factor. 

Log.Fac 

Arg.I 

Factor. 

Log.  Fin- 

Arg.I 

Factor 

L  igl-'iic 

Arg.I 

Factor. 

Log.Fac. 

Arg.I 

Fact 

L.  Fac. 

d 
0 

—  0.000 

n      CO 

d 

63 

—  12.596 

al  .1002 

d 

120 

+  2.049 

0.4231 

d 

180 

+12.109 

1.0831 

d 

0 

+0.00 

CO 

1 

<>.:!<;  r 

9.5575 

61 

1  2.547 

1.0985 

121 

2.990   0.1757 

181 

11.996 

1  .0790 

4 

0.22 

9.349 

a 

0.721 

9.8579 

62 

12.488 

1.0905 

122 

3.328    0.5222 

182 

1  1  .875 

1  .0746 

8 

0,14 

9.043 

3 

1.081 

0.0338 

63 

12.421 

1.0942 

123 

3.063 

0.5638 

183 

11.744 

1  .0698 

12 

0.06 

9.820 

4 

—  1.441 

j/0.1587 

64 

—12.343 

7(1.0914 

124 

+  3.997 

0.6017 

184 

+1  1  .604 

1.0040 

16 

+0.87    9.933 

5          1.7IH) 

0.2550 

65 

1  2.256 

1.0883 

125 

4.320   0.0301 

185 

11.454 

1  .0590 

80 

1.06 

0.027 

6 

2.156 

0.3331 

66 

12.159 

1.0849 

126 

4.052 

0.6670 

136 

11.295 

1  .0529 

24 

1  .25 

0.096 

7 

2.509 

0.3i)95 

67 

12.053 

1.0811 

127 

4.976 

0.0969 

187 

11.128 

1.0404 

28 

1.42 

0.151 

8  I—  2.S62 

;i0.4567 

68 

—  11.938 

nl.076!) 

128 

-f-  5.295 

0.7239 

1S8 

+10.952 

1.0395 

32 

+1.56 

0.194 

!) 

3.212 

0.51)68 

69 

11.813 

1  .0724 

129 

5.6II1  0.7490 

189 

10.706 

1.0321 

30 

1  .69 

0.22!) 

Ill 

3.563 

0.5514 

70 

11.680 

1  .0074 

130 

5.922    0.7725 

190 

10.571 

1.0241 

49 

1.80 

0.250 

11 

3.1)04 

0.5915 

71 

11.536 

1.0621 

131 

6.230 

0.7945 

191 

10.36!) 

1.0157 

44 

1.89 

0.277 

19 

—  4.210 

((9.02.-<9 

72 

—11.385 

n  1.0563 

132 

+  6.532 

0.8150 

192 

+10.158 

1.0068 

48 

+1.95 

0.291 

13 

4.584 

0.6612 

73 

1  1  .220 

1  .0502 

133 

6.829 

0,834  1 

193  i       9.939 

0.9973 

52 

1.99 

0.299 

14 

4.918 

0.6918 

74 

1  1  .056 

1.0436 

134 

7.121 

0.8525 

194 

9.712 

0.9-73 

50 

2.01 

0.302 

15 

5.250 

0.7202 

75 

10.S79 

1.0366 

135 

7.408 

0.8697 

195 

9.478 

0.9767 

6J 

1.9!) 

0.300 

Hi 

—  5.."7."> 

?i0.746a 

76 

—10.694 

n  1.0291 

136 

+  7.089 

0.8859 

196 

+  9.235 

0.0654 

61 

+  1.96 

0.292 

17 

5.8116 

0.7706 

77 

10.591 

1.0212 

137 

7.!  165 

0.9012 

197 

8.985 

0.9535 

68 

1.90 

0.273 

18 

6513 

0.7933 

78 

10.29!) 

1.0128 

138 

8.235 

0.9157 

198 

8.727 

0.9409 

72 

1.81 

0.253 

1!) 

6.524  . 

0.8145 

7!) 

10.090 

1.0039 

139 

8.498 

0.9293 

199 

8.463 

0.9275 

70 

1.71 

0.232 

30 

—  6.839 

nO.8344 

8!) 

—  9.873 

nO.!)944 

140 

-f-  8.756 

0.9423 

200 

+  8.191 

0.91  "S3 

80 

+1.58 

0.1  98 

21 

7.131 

0.85:!  1 

81 

9.048 

0.9844 

141 

9.006 

0.9545 

201 

7.914 

0.8984 

84 

1.43 

0.155 

22 

7.42G 

0.8707 

82 

9.417 

0.973!) 

142 

9.219 

0.9601 

202 

7.62!) 

0.8825 

88 

,   1.26 

0.101 

23 

7.715 

0.8873 

83 

9.177 

0.9627 

143 

9.486 

0.9771 

203 

7.338 

0.8656 

92 

1.03 

0.034 

24 

—  7.997 

rtO.9029 

84 

—  8.932 

nO.9509 

144 

-f  9.710 

0.9875 

204 

+  7.042 

0.8477 

96 

+9.88 

9.947 

as 

8.273 

0.9177 

85 

8.079 

0.9385 

145 

9.939 

0.9973 

205 

6.739 

0.8286 

100 

0.68 

!  1.832 

26 

8.542 

0.9316 

86 

8.421 

0.9254 

146 

10.153 

1.0066 

206 

6.431 

0.8083 

104 

0.46 

9.687 

27 

8.805 

0.9417 

87 

8.155 

0.9114 

147 

10.300 

1.0154 

2J7 

0.118 

0.7860 

108 

0.24 

9.380 

28 

—  9.060 

H0.9571 

88 

—  7.883 

7(0.8967 

148 

+  111.559 

1  .0236 

208 

+  5.801 

0.7635 

112 

+0.02 

i(8.293 

2!) 

9.308 

0.9689 

89 

7.006 

0.8812 

149 

10.750 

1.0314 

209 

5.478 

0.7386 

116 

-0.207t9.3IO 

30 

9.548 

0.9799 

90 

7.323 

0.8047 

1  50 

10.933 

1.0337 

210 

5.150 

0.7118 

120 

0.42 

9.029 

:u 

9.781 

04)904 

91 

7.035 

0.8473 

151 

11.108 

1.0456 

211 

4.819 

0.6830 

124 

0.04 

9.807 

32 

—  10.00.". 

n  1.0002 

92 

—  6.741 

nO.8287 

152 

+  11.274 

1.0521 

212 

+  4.484 

0.6517 

128 

—0.85 

«!  1.929 

33 

10.22:) 

1.0096 

93 

6.442 

0.8090 

153 

1  1  .432 

1.0581 

213 

4.145 

0.6175 

132 

1  .05 

0.020 

34 

lo.4:ii 

1.0183 

94 

6.138 

0.788  i 

154 

11.581 

1  .0037 

214 

3.802 

0.5800 

136 

1  .23 

0.091 

35 

10.031 

1.0266 

95 

5.S30 

0.7657 

155 

11.721 

1  .0690 

215 

3.457 

0.5387 

140 

1.40 

0.140  . 

36 

—10*03 

>il.  0343 

96 

—  5.517 

nO.7417 

156 

•fll.851 

1  .0738 

216 

+  3.108 

0,1925 

144 

—  1  .55 

«.0.19I 

37 

11.005 

1.0416 

97 

5.200 

0.710!) 

157 

1  1  .972 

1  .0782 

217 

2.757 

1)  1ID1 

148 

1.68 

0.226 

38 

11.179 

1.0484 

98 

•\~7:.< 

0.6883 

158 

12.085 

1.0S22 

218 

2.404 

0.3800 

152 

1.80 

0.254 

39 

11.344 

1  .05  18 

99 

4.555 

0.0585 

159 

18.189 

1.0800 

219 

2.049 

OJB115 

156 

1.89 

0.275 

40 

—11.500 

nl.0607 

100 

—  4.227 

7(0.0260 

160 

+12.283 

1  .0893 

220 

+  1.091 

0.2281 

160 

—1.95 

nO.290 

41 

M.(il7 

1  .0662 

101 

3.897 

0.5!!.,  7 

161 

12.367    1.0923 

221 

1  .333 

0.1248 

161 

1.99 

0.2!  19 

42 

1  1  .784 

.      .0713 

102 

3.563 

0.55  H 

162 

12.442 

1.0949 

222 

0.974 

9.9886 

168 

2.01 

0.302 

43 

11.91:! 

1  .0760 

103 

3.227 

0.5088 

163 

12.507 

1.0972 

223 

0.613 

9.7875 

172 

2.00 

0.300 

44 

—12.031 

•«  1.0803 

104 

—  2.^8 

7(0.4606 

164 

+12.563 

1  .0991 

224 

+  0.253 

7/1.4031 

176 

—1.96 

((0.293 

45 

12.140 

1.0842 

105 

2.547 

0.406') 

165 

12.60!) 

1.1007 

225 

—   0.198 

7(9.0334 

180 

1.90 

0.280 

46 

12.839 

1  .0877 

106 

2.205 

0.3434 

166 

12.015 

1.1019 

226 

0,109 

9.6712 

184 

1.82 

0.209 

47 

12.329 

1.0909 

107 

1.860 

0.2095 

167 

12071 

1.1028 

227 

0.829 

9.9185 

183 

1.72 

0.234 

48 

—12.408 

7(1.0937 

108 

—  1.514 

1(0.1^01 

168 

+12.087 

1.1034 

228 

—  1.189 

nO.0752 

192 

—  1.59 

nO.201 

4!) 

12.47!) 

1  .0962 

109 

1.167 

0.0071 

169 

12.693    1.1036 

229 

1  .548 

0.1898 

196 

1.44 

0.159 

50 

12.540 

1.0983 

110 

0.819 

9.91  33 

170 

12.690    1.1935 

230 

1.9D6 

0.280  1 

200 

1  .2.8 

0.100 

51 

12.5!  10 

1.1000 

111 

0.471 

9.0730 

171 

12.676    1.1030 

231 

2.202 

0.3545 

204 

1.10 

0.040 

52 

—12.630 

7(1.101  1 

112 

—  0.122 

H.9.0804 

172 

+12.653    1.1022 

232 

—  2.615 

wO.4175 

208 

—0.90 

B9.9S6 

53 

12.660 

.1024 

113 

+  0.227 

p9.3560 

173 

12.61!)    1.1010 

333 

2.967 

0,1723 

212 

0.70 

9.843 

54 

12.681 

.1032 

114 

0.575 

9.7597 

174 

12.576    1.0995 

234 

3.317 

0.5207 

216 

0.48 

9.684 

55 

12.602 

.1035 

115 

0.983 

9.9052 

175 

12.522 

1.0977 

235 

3.664 

0.5640 

220 

0.26 

9.420 

56 

—12.692 

7(  .K;:!.-. 

116    +  1.271 

0.1011 

170 

+  12,159 

1  .0955 

236 

—  4.007 

»0j6028 

224 

—0.04 

H«.59I 

57 

12.683 

.1032 

117 

1.617 

0.2087 

177 

12.386    1.0929 

237 

4.348 

0.6383 

228 

+0.18  p9.267 

08 

13.664 

.1026 

118 

U>63 

0.2:12.1 

178 

12.3)1     1.0900 

233 

4.685 

0.6707 

232 

0.11     9.(i09 

09 

12.635 

.1016 

119 

2:307 

0.3630 

17!) 

12.211     1.086U 

239 

5.018 

0.7.105 

236 

0.02 

9.795 

60 

—  12.5!  6 

»   .10(12 

120 

+  2.649 

0.4231 

IS;) 

+  12.109    1.0831 

219 

—  5.319 

7(0.7283 

21:)    +0.83 

9.920 

The  perturbations  arc  expressed  in  limulrcdllis  of  a  second  of  arc. 


TAHLKS. 


TABLE   XIII. 

r  vui.i:  xiv. 

TAIILK   XV. 

TAIU.I:  xvi. 

I'trt.  tif  thr   1.  illicit  Hill   I'll  Ilir 
I'.iirth. 

I'rrt.  of  llit  /.«' 

/«./,,  /•;/  M 

I'irlurlialiiiH  (if  III  r  l.,inyilinlr, 
by  t/ir  I-'.:,  rill. 

/'«  rt  nrl'iifnut  tif'  flit    l.int^tlittl',  />i/  t!i<- 
'  Larth. 

Arg   II 

,:„„, 

Arg    II. 

Arg.  Ill 

Ar«    IV. 

t\ 

Eqan. 

Ar"    V. 

,:„„, 

» 

• 

,1 

,1 

,i 

,i 

d 

0 

0 

•Jlo 

n 

II 

0 

2960 

0 

2 

736 

707 

9 

0 

900 

10 

I 

2920 

16 

.-, 

758 

708 

4 

i 

836 

400 

913 

m 

3 

88 

|) 

768 

708 

6 

3 

234 

600 

804 

190 

.-, 

2-10 

i- 

15 

7-1 

707 

8 

"' 

839 

194 

n.i 

9 

64 

23 

-;IO 

703 

10 

9 

230 

ten 

I.-3 

2  HI 

il 

9760 

-0 

89 

816 

I-J 

13 

228 

1800 

171 

840 

in 

9780 

96 

43 

6UI 

14 

17 

886 

1  100 

158 

880 

96 

21,-  I 

118 

55 

848 

683 

Hi 

23 

._,.,  | 

10:10 

145 

32  1 

34 

186 

864 

678 

18 

•-".1 

889 

1- 

131 

12 

1  11 

880 

663 

90 

86 

990 

20IKI 

117 

400 

.->! 

9660 

Kill 

M 

(i!7 

29 

n 

918 

22,  M  I 

103 

110 

61 

2-VJ.l 

176 

II., 

918 

639 

84 

68 

816 

9400 

90 

480 

71 

2480 

199 

l:;2 

988 

615 

26 

(il 

214 

9600 

7(i 

:,2  1 

83 

211  I 

151 

944 

507 

28 

70 

819 

9800 

64 

560 

94 

22  1 

170 

960 

.',77 

30 

80 

910 

3000 

89 

GOO 

106 

9960 

•Jill 

190 

976 

566 

32 

91 

206 

3800 

41 

640 

118 

8320 

956 

210 

998 

534 

34 

109 

3400 

89 

680 

131 

22-0 

272 

231 

loos 

511 

36 

II  1 

804 

3600 

93 

790 

1  II 

2210 

888 

259 

1084 

4-i, 

38 

126 

808 

3800 

16 

TOO 

156 

, 

304 

273 

1040 

461 

40 

199 

•j  i,  i 

4000 

10 

BOO 

169 

9160 

890 

1056 

4:w; 

42 

I  :,2 

198 

4800 

5 

-n 

181 

2120 

336 

317 

1072 

411) 

II 

165 

106 

1100 

2 

880 

mi 

8080 

369 

339 

1088 

383 

46 

179 

194 

4600 

(1 

090 

206 

8040 

86S 

360 

1104 

856 

48 

193 

199 

HMO 

0 

'.Kill 

217 

884 

389 

1120 

880 

50 

190 

5000 

0 

1000 

998 

I960 

400 

404 

1136 

303 

69 

221 

188 

2 

loin 

239 

1980 

416 

12", 

1168 

271  i 

64 

2:!6 

l-t, 

5400 

:, 

lu-il 

949 

1880 

438 

•i  Hi 

116--! 

2-">0 

66 

950 

1-1. 

5QOO 

I) 

1120 

1840 

4  is 

467 

11-1 

286 

58 

265 

Id2 

5800 

14 

1160 

266 

1800 

464 

487 

1200 

200 

GO 

280 

180 

6000 

20 

1200 

271 

1760 

480 

507 

1216 

177 

62 

995 

178 

6200 

26 

1240 

•J-n 

1720 

496 

.-,27 

1232 

164 

64 

310 

176 

6400 

34 

1980 

986 

1680 

619 

54.') 

121- 

133 

66 

32  1 

171 

6600 

42 

1390 

891 

1640 

598 

563 

1864 

113 

i,s 

339 

172 

6800 

50 

1360 

898 

1600 

644 

581 

1280 

94 

70 

3.-.3 

170 

7000 

89 

1400 

297 

1560 

560 

597 

12!Ki 

77 

72 

368 

168 

(in 

1  110 

909 

1590 

676 

613 

1312 

61 

74 

889 

166 

7400 

78 

1480 

299 

1480 

099 

628 

1388 

47 

76 

395 

164 

7600 

88 

1,11 

IS44 

3.-> 

78 

409 

169 

7800 

00 

624 

694 

1360 

2T> 

80 

422 

160 

8000 

1IMI 

(ill) 

666 

1876 

17 

82 

434 

1  .- 

8200 

120 

656 

(>7(> 

1399 

10 

84 

447 

156 

8400 

131 

672 

1  Ins 

.', 

86 

450 

164 

8600 

141 

(,  —  : 

693 

1  121 

3 

88 

470 

188 

8800 

189 

7.11 

699 

1110 

2 

90 

481 

160 

9000 

Ki2 

720 

703 

1  i:.6 

3 

92 

491 

148 

9200 

172 

736 

707 

1472 

5 

M 

.Mil 

146 

9400 

189 

96 

r.io 

ill 

0600 

1  :  i-' 

98 

518 

149 

9800 

200 

n 

100 

526 

140 

1  0000 

Constant  added  in  Table  XIII.      2-2 

102 

633 

138 

10200 

2lli 

••        "     XIV.      Li:.. 

104 

539 

136 

10400 

299 

<•              ••       11        ••     XV.        l.:,o. 

106 

645 

134 

10600 

227 

"       11        »     XVI.     3.60. 

108 

550 

132 

10800 

231 

110 

554 

130 

11000 

234 

y 

558 

128 

11200 

286 

Period  of  Argument  II.                  238.92. 

114 

660 

1  26 

11400 

935 

"ii            »         III.                 11987'!. 

116 

562 

124 

11600 

233 

"      "            •«         IV.                   29.W 

118 

564 

122 

11800 

230 

u      it            n         v.                     1454<>9. 

120 

564 

120 

12000 

916 

• 

9V 


The  perturbations  arc  expressed  in  liuiiilri-<lili>  ol'n  nerond  of  arc. 


TABLE   XVII. 


Perturbation  of  I  lie  Longitude  l>y  I  lie  Earth. 

Constant  ;:ililoil  16".65.            Period  of  Argument  VI.,  583''.92. 

Arg.  VI. 

Equa. 

Arg.  VI. 

Equa. 

Arg.  VI. 

Equa. 

Arg.  VI. 

Eqlia; 

Arg.  VI. 

Equa. 

Arg.  VI. 

Equa. 

d 

d 

d 

d 

d 

d 

0 

166-i 

104 

47 

208 

8720 

312 

912 

416 

2093 

520 

2456 

2 

1671 

106 

31 

210 

2772 

314 

846 

413 

2172 

522 

2405 

4 

1675 

108 

18 

212 

2821 

316 

783 

420 

224!) 

524 

2354 

6 

1677 

110 

8 

214 

2366 

318 

722 

422 

2326 

526 

2303 

8 

1670 

112 

3 

216 

2908 

320 

664 

424 

2400 

528 

2254 

10 

1680 

114 

0 

218 

2946 

322 

609 

426 

2473 

530 

2205 

19 

1678 

116 

2 

220 

2979 

324 

557 

428 

2544 

533 

•>  1  5s 

14 

1676 

118 

7 

222 

3009 

326 

509 

430 

2613 

534 

2112 

16 

1671 

120 

16 

224 

3035 

328 

464 

432 

2680 

536 

2068 

18 

1664 

122 

28 

226 

3057 

33!) 

423 

434 

2744 

538 

2025 

20 

1655 

ISM 

4") 

228 

3074 

332 

385 

436 

2805 

540 

1985 

o-> 

1043 

126 

65 

230 

3087 

334 

352 

438 

2863 

542 

1946 

24 

1623 

128 

90 

232 

3095 

3.36 

322 

440 

2918 

544 

1910 

26 

1611 

130 

118 

234 

3099 

338 

296 

442 

2!  171 

546 

1875 

as 

1591 

139 

149 

236 

3099 

340 

275 

444 

3020 

548 

1843 

30 

1569 

134 

185 

238 

3095 

342 

258 

446 

3065 

550 

1813 

32 

1544 

136 

824 

240 

3086 

344 

245 

448 

3108 

552 

1786 

34 

1517 

138 

266 

242 

3073 

346 

237 

450 

3147 

554 

1762 

36 

1486 

140 

312 

244 

3055 

348 

233 

452 

3188 

556 

1740 

38 

1454 

142 

361 

246 

3033 

350 

233 

454 

3214 

558 

1721 

40 

141!) 

144 

414 

248 

3007 

352 

237 

456 

3241 

560 

1704 

42 

1382 

146 

470 

250 

2977 

354 

246 

458 

3265 

569 

1690 

44 

1343 

148 

523 

252 

2943 

356 

259 

460 

3285 

564 

167!) 

46 

1302 

150 

590 

254 

2905 

358 

277 

462 

3302 

566 

1670 

48 

1250 

152 

654 

256 

2864 

360 

299 

464 

3314 

568 

1663 

50 

1314 

154 

720 

258 

2818 

362 

325 

466 

3323 

570 

1659 

52 

1168 

156 

789 

260 

2770 

364 

355 

468 

3328 

572 

1656 

54 

1120 

158 

860 

262 

2717 

366 

389 

470 

3329 

574 

1655 

56 

107! 

160 

933 

264 

2662 

368 

426 

472 

3327 

576 

1656 

58 

10x22 

162 

1008 

266 

2604 

370 

468 

474 

3320 

578 

1638 

60 

971 

164 

1084 

263 

2542 

372 

514 

476 

331  1 

580 

1661 

62 

920 

166 

1162 

270 

2479 

374 

563 

478 

3297 

582 

1664 

64 

863 

168 

1241 

272 

2412 

376 

615 

480 

3280 

584 

1668 

66 

816 

170 

1321 

274 

2344 

378 

671 

482 

3260 

586 

1671 

68 

764 

172 

1409 

876 

2273 

380 

729 

484 

3237 

588 

1675 

70 

712 

174 

14o3 

278 

2201 

382 

791 

486 

3211 

590 

1677" 

72 

6GO 

176 

1564 

280 

2127 

384 

855 

488 

3189 

592 

1679 

74 

60!) 

178 

1646 

282 

2051 

386 

929 

490 

3150 

594 

1630 

76 

559 

180 

1727 

284 

1975 

388 

091 

492 

3116 

596 

1678 

78 

510 

182 

1808 

286 

1897 

390 

1063 

494 

3079 

598 

1676 

80 

462 

184 

1888 

288 

1819 

392 

1137 

4% 

3039 

600 

1671 

82 

415 

186 

1967 

290 

1740 

394 

1212 

498 

2998 

602 

1664 

84 

370 

188 

21146 

292 

1661 

396 

128!) 

500 

9054 

604 

1655 

86 

327 

]'.)() 

2123 

294 

1582 

398 

1367 

502 

290!) 

606 

1642 

88 

285 

192 

2198 

296 

1504 

400 

1446 

504 

2862 

608 

1627 

90 

246 

194 

2272 

298 

1426 

402 

1527 

506 

2814 

610 

1610 

99 

210 

196 

2343 

300 

1348 

404 

1607 

508 

2764 

612 

1590 

!)4 

175 

198 

2413 

302 

1272 

406 

1689 

510 

2714 

614 

1568 

'.16 

144 

200 

2479 

304 

1197 

408 

1770 

512 

2663 

616 

1543 

98 

115 

202 

2544 

306 

1193 

410 

1851 

514 

2612 

618 

1516 

100 

89 

204 

2605 

3(18 

1051 

412 

1932 

516 

2560 

620 

1485 

102 

67 

206 

266-1 

310 

980 

414 

2013 

518 

2508 

622 

1  153 

104 

47 

208     2720 

312 

912 

416 

2093 

520 

2156 

624 

1418 

The  perturbations  are  expressed  in  liimdrcdtlis  of  a  second  of  arc. 

TAI1L.KS. 


E   1155.1      XVIII. 

TAKM-:   XIX. 

>^*cT0^E^3 
Till  l,i:   XX.     / 

J  N  J  W  T3  i 

l'i  rt.  of  tin-  Litnaitinli- 
liy  lli<-  F.nrlli. 

1'i-rt.  n!  Hi,-  Lnin;i/iifli- 
l'i/   Mnrx. 

Perturbation  »/'  the  Lon^innli-  Ay  jionVfrX  &  il 

\c 

^         7PAT3- 

Arg.  VII 

Equa. 

Art;   VII. 

Ar-  \  III 

,,„,, 

Ar|  \  III 

Arg.  IX. 

,,,,,. 

Arg.  IX. 

Equa. 

"»t 
Arg.  IX. 

d 
0 

il 

948 

d 
0 

0 

.1 
934 

d 

0 

339 

d 

-H 

7 

Kill' 

1,71 

4 

0 

'.Ml 

4 

0 

._,._,,  , 

2 

:iv!7 

-J 

19 

169 

672 

8 

8 

940 

8 

1 

916 

4 

:i-M 

-1 

P.I 

161 

1,7'.' 

19 

•"' 

936 

19 

:l 

212 

6 

316 

96 

98 

166 

67(1 

Hi 

10 

939 

16 

6 

8 

300 

as 

168 

667 

80 

16 

22* 

90 

B 

•_'.  '  1 

HI 

303 

'.Ml 

10 

170 

663 

24 

96 

22  1 

94 

13 

21  Ml 

19 

996 

09 

69 

179 

98 

34 

mo 

88 

l- 

106 

1  1 

•J-:' 

04 

77 

171 

6T.1 

38 

46 

916 

39 

93 

199 

16 

981 

06 

83 

176 

643 

36 

57 

919 

36 

99 

I-- 

18 

27:1 

no 

17- 

634 

•in 

71 

•jn- 

III 

1-1 

-'n 

2(il 

mo 

198 

1-  i 

694 

II 

* 

804 

II 

49 

i-  1 

99 

856 

109 

1  i- 

189 

613 

18 

100 

200 

|8 

50 

176 

94 

845 

104 

168 

l-l 

59 

116 

196 

59 

57 

172 

26 

935 

106 

100 

186 

600 

56 

1  32 

199 

56 

(il 

168 

28 

-.'-.'  1 

in- 

919 

]-- 

577 

60 

149 

188 

Gil 

72 

164 

30 

213 

lli) 

936 

100 

164 

64 

163 

1    1 

64 

70 

160 

32 

901 

119 

950 

199 

RBI 

6d 

i-j 

ISO 

&s 

96 

156 

34 

188 

III 

883 

1:14 

.->:'.- 

79 

108 

176 

7-.' 

08 

159 

36 

171, 

116 

807 

196 

76 

915 

172 

76 

ion 

1  1- 

38 

163 

118 

332 

198 

511 

930 

168 

80 

106 

III 

•HI 

150 

PJI 

356 

800 

I    - 

84 

946 

164 

84 

119 

140 

49 

137 

122 

:;-i 

909 

!     , 

88 

950 

160 

88 

117 

1  .:i  > 

44 

123 

124 

405 

204 

472 

09 

979 

[56 

!I2 

121 

139 

46 

110 

196 

428 

206 

|i,i 

IK; 

963 

152 

% 

125 

198 

48 

08 

198 

159 

908 

448 

100 

804 

1  1- 

100 

198 

124 

50 

96 

130 

471 

210 

436 

104 

303 

1  II 

Illl 

130 

120 

59 

73 

189 

486 

919 

496 

108 

310 

140 

108 

131 

116 

54 

62 

134 

517 

21  1 

•      415 

119 

316 

136 

119 

132 

112 

56 

51 

136 

537 

216 

405 

116 

321 

138 

58 

41 

138 

556 

918 

386 

190 

323 

12- 

<>0 

38 

140 

r,7:l 

990 

::-- 

194 

894 

194 

62 

23 

142 

BOO 

222 

64 
6G 

16 

10 

1  II 

i  it; 

GII:> 
618 

224 
996 

372 
365 

se 

6 

148 

630 

998 

350 

70 

2 

150 

611 

230 

88i 

72 

0 

169 

850 

232 

346 

74 

0 

154 

658 

234 

311 

76 

0 

156 

664 

836 

335 

78 

3 

158 

668 

330 

80 

7 

160 

671 

240 

394 

"                                                                                             t 

Constant  added  in  Table  XVIII.    1.62.                                                Period  of  Argument  VII.     213.16. 

Constant  added  in  Table  XIX.       IMJ6.                                                    Period  of  Argument  VIII.   220.57. 

Constant  added  in  Table  XX.         3.35.                                                    Period  of  Argument  IX.      a36.!>!i. 

The  perturbations  are  expressed  in  liundredths  of  a  second  of  arc. 

3O 


TABLE  XXI. 


Perturbation  of  the  Longitude  by  Mercury. 

Horizontal  Argument  =  I. 
Constant  added  0''.85.          Period  of  Argument  1.,  224''  .7. 

tl 

d 

d      cl 

d 

rt 

<] 

d 

d 

rt 

d 

d 

d 

d 

d 

Arg.  X 

0 

§ 

16 

24 

32 

40 

48 

56 

64 

72 

80 

88 

96 

104 

112 

0 

139 

131 

131 

132 

135 

137 

138 

138 

138 

141 

146 

152 

158 

162 

162 

J 

I'M 

127 

128 

129 

138 

134 

134 

135 

136 

139 

144    151 

156 

158 

158 

2 

123 

122 

122 

124 

127 

139 

130 

131 

138 

136 

142 

148 

158 

153 

152 

3 

116 

lir> 

116 

118 

121 

121 

125 

125 

128 

132 

138 

143 

147 

116 

143 

4 

1(17 

107 

100 

112 

115 

117 

118 

120 

122 

127 

133 

138 

139 

138 

134 

6 

99 

99 

102 

105 

108 

111 

112 

113 

117 

122 

127 

131 

131 

128 

123 

6 

90 

91 

EM 

98 

102 

104 

105 

107 

III 

116 

121 

123 

122 

118 

112 

7 

81 

84 

87 

92 

95 

97 

99 

llll 

105 

110 

114 

115 

112 

107 

100 

8 

74 

77 

81 

86 

89 

92 

93 

96 

100 

104 

107 

107 

102 

96 

89 

9 

67 

72 

76 

81 

86 

87 

88 

91 

95 

99 

100 

99 

93 

85 

78 

in 

63 

68 

73 

78 

81 

83 

85 

87 

ill 

94 

94 

91 

84 

76 

68 

M 

60 

60 

71 

75 

79 

80 

82 

85 

88 

90 

89 

.-'1 

76 

67    60 

13 

59 

65 

70 

?•"» 

77 

79 

81 

83 

86 

86 

84 

78 

69 

6U 

53 

13 

60 

(ili 

72 

76 

78  i    79 

80 

83 

S4 

84 

80 

73 

63 

55 

48 

14 

61 

70 

75 

78 

80 

81 

82 

83 

6M 

82 

77 

69 

59 

51 

45 

IS 

68 

75 

79 

§8 

83 

83 

84 

85 

85 

81 

75 

66 

57 

49 

43 

Hi 

75 

81 

85 

86 

87 

87 

87 

87 

86 

81 

74 

65 

56 

49 

44 

17 

84 

88. 

91 

92 

92 

91 

91 

91 

88 

82 

74 

65 

56 

50 

46 

18 

!)3 

97 

9!) 

98 

97 

96 

96 

94 

90 

84 

75 

(ir. 

57 

52 

58 

19 

102 

106 

106 

105 

103 

102 

100 

98 

93 

85 

76 

67 

60 

56 

55 

20 

na 

ill 

113 

111 

109 

107 

105 

101 

95 

87 

78 

69 

64 

61 

60 

21 

181 

122 

120 

117 

114 

112 

108 

104 

98 

89 

80 

72 

68 

66 

66 

22 

130 

129 

126 

122 

119 

115 

112 

107 

99 

90 

81 

75 

72 

71 

72 

23 

137 

135 

131 

126 

122 

118 

114 

108 

100 

91 

83 

78 

76 

77 

78 

24 

143 

139 

134 

129 

124 

120 

115 

108 

100 

91 

84 

80 

.80 

81 

83 

25 

147 

143 

136 

130 

125 

120 

114 

108 

99 

91 

85 

82 

83 

85 

88 

26 

148 

142 

135 

129 

123 

118 

113 

105 

97 

89 

84 

83 

85 

88 

91 

27 

147 

140 

133 

126 

120 

115 

109 

101 

93 

87 

83 

83 

87 

90 

93 

28 

'  144 

136 

128 

121 

111, 

110 

104 

96 

89 

83 

81 

83 

87 

90 

93 

29 

138 

130 

122 

115 

109 

104 

97 

90 

83 

79 

78 

81 

86 

89 

92 

30 

130 

122 

113 

107 

101 

96 

89 

82 

77 

74 

75 

78 

83 

87 

89 

31 

120 

112 

101 

98 

92 

87 

80 

74 

69 

68 

70  !    75 

80 

83 

85 

'  32 

109 

1011 

93 

87 

82 

77 

71 

65 

62 

62 

65 

70 

75 

78 

80 

33 

96 

88 

81 

75 

71 

66 

61 

56 

54 

56 

60 

65 

70 

73 

74 

34 

82 

74 

68 

64 

60 

55 

51 

47 

46 

49 

54 

60 

64 

66 

68 

35 

68 

61 

56 

68 

49 

45 

41 

39 

39 

43 

49 

54 

58 

60 

61 

36 

54 

48 

41 

41 

38 

35 

33 

31 

33 

38 

44 

49 

52 

53 

54 

37 

41 

36 

33 

31 

29 

26 

24 

25 

28 

33 

39 

44 

46 

47 

47 

38 

29 

26 

24 

22 

21 

19 

18 

19 

24 

30 

36 

39 

41 

41 

42 

39 

19 

17 

16 

13 

14 

13 

13 

16 

21 

27 

33 

36 

37 

37 

37 

40 

11 

10 

10 

10 

10 

10 

11 

14 

20 

26 

31 

34 

34 

34 

34 

41 

5 

5 

6 

7 

8 

8 

10 

15 

21 

27 

31 

33 

32 

32 

32 

42 

2 

3 

5 

7 

8 

9 

12 

17 

23 

29 

32 

33 

32 

32 

33 

43 

2 

4 

6 

9 

10 

12 

15 

21 

27 

32 

35 

35 

34 

34 

35 

44 

4 

7 

10 

12 

14 

17 

21 

27 

33 

37 

39 

39 

37 

37 

39 

45 

8 

12 

16 

19 

21 

24 

29 

35 

40 

44 

44 

43 

42 

43 

45 

46 

16 

20 

24 

27 

89 

33 

38 

43 

48 

51 

51 

50 

49 

50 

53 

47 

25 

30 

34 

36 

39 

43 

48 

53 

58 

59 

59 

57 

57 

58 

62 

48 

36 

41 

45 

47 

50 

54 

59 

64 

68 

68 

67 

66 

66 

68 

72 

49 

48 

53 

57 

59 

62 

66 

71 

75 

78 

78 

77 

75 

76 

79 

84 

50 

61 

65 

69 

71 

74 

78 

82 

86 

88 

88 

86 

85 

87 

91 

96 

51 

74 

78 

81 

83 

86 

91) 

94 

97 

98 

97 

96 

96 

98 

103 

108 

52 

87 

91 

93 

95 

97 

101 

105 

107 

JOS 

106 

1(15 

106 

109 

115 

120 

53 

99 

11)2 

104 

105 

108 

III 

114 

116 

116 

115 

114 

116 

120 

126 

138 

54 

110 

112 

113 

114 

117 

120 

123 

124 

124 

122 

122 

125 

130 

136 

142 

55 

119 

•j\ 

121 

122 

124 

27 

130 

131 

130 

129 

130 

133 

139 

145 

150 

56 

126 

27 

127 

128 

130 

33 

135 

135 

135 

134 

136 

140 

146 

153 

157 

57 

I3J 

31 

131 

139 

134 

37 

138 

139 

138 

138 

141 

145 

1  .vj 

158 

162 

58 

134 

34 

133 

134 

136" 

39 

140 

140 

139 

140 

144 

149 

156 

161 

164 

59 

134 

33 

133 

134 

137 

30 

140 

140 

140 

141 

146 

152 

158 

163 

Kit 

GO 

132 

31 

131 

132 

135 

137 

138 

138 

138 

141 

M6 

158 

168 

162 

162 

The  perturbation!  are  expressed  in  hundredllis  of  a  second  of  arc 


TABLE   XXI. 


31 


Perturbation  <>f  tin-  Longitude  l>n  Mercury. 

Constant  iidili-d  ,                                                !  ,,f  Argument  X  ,  60. 

d 

,l 

d 

d 

d 

d 

d 

d 

.1 

d 

,1 

d 

,1 

d 

120 

12W 

136 

111 

1.12 

160 

16* 

176 

1!>2 

200 

20* 

216 

221 

2!I2 

0 

169 

160 

159 

1  .- 

166 

181 

146 

138 

130 

194 

110 

III 

108 

'.ill 

H 

1 

156 

154 

159 

ISO 

II? 

111 

134 

195 

1  1* 

ill 

106 

'.i? 

BO 

79 

:•'. 

2 

1  l:i 

IK, 

143 

Mil 

136 

190 

190 

112 

Ml 

;i? 

HI 

71 

59 

3 

1  10 

136 

1:1:1 

199 

193 

115 

Ml, 

97 

90 

76 

60 

.M 

Ii, 

4 

190 

12.-> 

121 

116 

100 

100 

!l| 

-J 

7.') 

69 

62 

54 

46 

3!) 

34 

5 

II- 

113 

108 

102 

,,;, 

76 

(il 

:,:, 

1- 

41 

:u 

27 

M 

6 

i-  6 

10| 

90 

80 

71 

54 

1- 

19 

36 

99 

98 

18 

16 

7 

94 

88 

89 

75 

G7 

.",? 

II 

;t| 

in 

14 

10 

9 

8 

82 

76 

70 

G:I 

r,l 

16 

91 

II, 

11 

7 

5 

5 

9 

71 

66 

59 

:,i 

41! 

84 

27 

M 

18 

11 

in 

6 

3 

2 

3 

10 

62 

56 

4!  > 

rj 

33 

86 

19 

16 

19 

hi 

6 

3 

2 

9 

4 

11 

61 

48 

41 

34 

21  i 

19 

II 

19 

ID 

8 

6 

3 

3 

5 

8 

12 

47 

42 

86 

98 

•JI 

Hi 

12 

II 

hi 

8 

7 

6 

7 

10 

14 

13 

42 

87 

31 

95 

1- 

11 

12 

19 

12 

12 

II 

11 

13 

16 

99 

11 

40 

m 

30 

24 

l!l 

Ii, 

16 

Hi 

17 

17 

17 

19 

a 

27 

89 

15 

39 

35 

30 

95 

21 

M 

20 

22 

21 

95 

26 

29 

33 

38 

43 

16 

40 

37 

32 

26 

M 

31 

33 

;;  | 

36 

40 

45 

50 

55 

17 

43 

40 

37 

84 

89 

34 

ft? 

40 

43 

46 

48 

52 

57 

63 

68 

18 

48 

45 

42 

41 

41 

43 

47 

57 

60 

6.'. 

71 

71, 

81 

19 

53 

49 

49 

50 

54 

58 

G:! 

66 

G'.l 

73 

78 

84 

89 

93 

20 

59 

58 

57 

57 

60 

65 

70 

74 

78 

81 

85 

91 

96 

101 

104 

21 

65 

66 

(M 

66 

70 

76 

81 

86 

89 

99 

97 

109 

107 

112 

114 

99 

72 

72 

7.-, 

-.1 

86 

91 

in; 

99 

lo:t 

107 

119 

117 

190 

122 

79 

711 

81 

84 

09 

96 

101 

106 

III 

116 

190 

196 

127 

128 

21 

84 

85 

88 

97 

103 

108 

112 

116 

118 

122 

127 

130 

132 

189 

2."> 

89 

90 

93 

98 

104 

110 

114 

118 

120 

121! 

127 

131 

183 

184 

134 

26 

92 

94 

98 

108 

109 

III 

118 

191 

193 

126 

129 

139 

134 

134 

133 

27 

94 

96 

100 

106 

119 

117 

120 

199 

12:! 

196 

199 

131 

139 

132- 

131 

96 

97 

101 

107 

119 

117 

119 

120 

122 

194 

196 

198 

199 

127 

126 

.;,, 

!tl 

96 

101 

106 

ill 

114 

116 

117 

118 

190 

122 

193 

193 

121 

120 

80 

91 

94 

98 

103 

108 

110 

111 

III 

119 

114 

116 

116 

115 

114 

113 

31 

87 

90 

94 

99 

103 

104 

106 

104 

in:. 

106 

1H7 

108 

107 

105 

105 

39 

B9 

85 

98 

96 

H7 

97 

96 

97 

98 

!l!l 

99 

98 

97 

97 

76 

79 

83 

86 

88 

88 

83 

87 

88 

89 

89 

8!) 

89 

88 

34 

69 

72 

76 

7!l 

80 

79 

78 

78 

78 

80 

80 

80 

80 

80 

81 

36 

62 

66 

63 

70 

71 

70 

69 

68 

70 

71 

72 

79 

71 

72 

7.-, 

3G 

58 

61 

63 

63 

61 

60 

60 

Gl 

63 

1,1 

64 

6.". 

66 

70 

49 

51 

54 

6fi 

56 

53 

52 

5.1 

55 

56 

.",7 

58 

59 

62 

66 

38 

43 

46 

48 

49 

48 

46 

46 

47 

49 

53 

54 

56 

50 

64 

39 

39 

41 

43 

43 

43 

42 

42 

43 

46 

4!) 

50 

69 

55 

59 

64 

40 

36 

38 

40 

40 

39 

38 

3!) 

42 

46 

48 

50 

69 

56 

61 

66 

41 

34 

37 

3D 

38 

38 

38 

89 

42 

46 

50 

59 

55 

69 

lil 

70 

49 

35 

37 

39 

39 

38 

39 

42 

46 

50 

.-,4 

56 

(II 

70 

7.') 

4:t 

37 

40 

41 

42 

42 

43 

47 

51 

56 

60 

63 

66 

71 

77 

•'-' 

44 

42 

44 

46 

46 

47 

50 

54 

64 

68 

71 

75 

79 

85 

90 

45 

48 

61 

52 

53 

55 

58 

63 

69 

73 

77 

80 

84 

89 

BO 

00 

46 
47 

56 
66 

-,'.i 
6!l 

61 
71 

62 
73 

64 
75 

68 
80 

71 
86 

-  1 

09 

-1 
06 

88 

99 

91 

102 

96 

106 

100 
110 

106 

III 

107 

116 

48 
49 

77 

88 

80 
92 

82 
94 

84 
97 

88 
101 

93 
106 

9!) 
112 

104 
117 

190 

111 
193 

114 
198 

117 
128 

191 

130 

194 

1  :.' 

194 
131 

50 

101 

104 
116 

106 
II!) 

110 
199 

114 
127 

11!) 
139 

125 

137 

12!) 
140 

139 

112 

133 
149 

135 

137 
14.') 

139 
146 

139 

III 

137 
111 

52 
53 
54 

195 

146 

128 

138 
148 

130 

III 
1.-.0 

134 
146 

138 

1  l'i 
167 

I  II 
I  :,:t 
161 

1  1- 
156 

ISO 
157 

163 

150 
157 

1GI 

160 
166 

I.V.I 

ISO 
155 
197 

150 
164 
158 

150 

158 
189 

148 

148 
147 

143 
143 
140 

55 
56 

to 

to 

60 

154 

160 

11)1 

16.-. 
162 

156 
161 
164 

166 
164 

160 

158 
169 
166 

166 
164 

159 

161 
166 

167 
1G7 
164 
188 

li>l 
168 
169 
167 

I56 

166 
169 
160 
163 

Ilil 
151 

167 

162 
I5S 
148 

165 
166 
169 
156 

1  1- 

161 

|50 
141 

130 

180 

159 
148 
136 
194 

1.-.7 
154 

II- 

1  M 
1    10 

II- 

154 

150 
143 
134 
193 
111 

i  ii 
187 
197 
116 

103 

113 
137 

r.- 
II- 

98 

136 
190 
190 

ion 

Add  33.26  to  Arg.  X   wln-n  224''.7  is  lubtracted  from  Arg.  I. 

TABLE  XXII. 


Perturbations  of  the  Longitude  by  the  Earth. 

Horizontal  Argument  =  I. 

Constant  added  1".40.          Period  of  Argument  I.  224(1.7. 

a 

d 

d 

d 

d 

d 

d 

d      d      d 

d 

a 

d      d     d 

Arg.XI 

0 

8 

16 

21 

32 

40 

48 

56 

61 

72 

§0 

§§ 

96 

IO1 

112 

0 

71 

80 

88 

94 

98 

100 

102 

105 

110 

117 

127 

140 

153 

165 

177 

1 

63 

71 

79 

85 

88 

90 

08 

95 

99 

105 

115 

126 

139 

152 

164 

2 

55 

63 

71 

76 

79 

81 

82 

85 

88 

94 

102 

113 

126 

138 

151 

3 

49 

56 

63 

6S 

71 

72 

::i 

75 

77 

82 

91 

101 

113 

126 

138 

4 

44 

50 

56 

60 

63 

64 

65 

66 

68 

72 

80 

90 

101 

114 

126 

5 

40 

45 

50 

54 

56 

57 

57 

56 

59 

63 

70 

79 

90 

102 

115 

6 

39 

42 

47 

50 

51 

52 

51 

51 

53 

55 

61 

70 

-1 

92 

105 

7 

39 

42 

45 

47 

48 

48 

47 

47 

47 

49 

54 

62 

72 

84 

95 

8 

42 

43 

46 

47 

47 

47 

45 

44 

43 

45 

49 

56 

65 

76 

87 

9 

47 

47 

48 

49 

49 

48 

45 

43 

42 

42 

45 

51 

60 

70 

81 

10 

54 

53 

53 

54 

53 

51 

48 

45 

43 

42 

44 

49 

56 

65 

75 

11 

63 

61 

01 

60 

59 

57 

53 

49 

46 

44 

45 

48 

54 

62 

71 

13 

73 

71 

70 

69 

67 

64 

61 

56 

51 

49 

47 

49 

53 

61) 

67 

13 

84 

83 

81 

80 

77 

74 

70 

64 

59 

55 

52 

52 

55 

59 

66 

14 

95 

94 

92 

91 

89 

85 

80 

74 

68 

62 

58 

57 

58 

61 

65 

15 

107 

106 

104 

103 

101 

97 

92 

85 

78 

72 

66 

63 

62 

63 

66 

16 

118 

117 

116 

115 

114 

10!) 

104 

97 

89 

82 

75 

70 

68 

67 

69 

17 

12!) 

IsM 

128 

127 

125 

121 

116 

108 

100 

92 

84 

78 

71 

73 

73 

18 

13d 

13d 

133 

137 

136 

132 

127 

119 

111 

102 

94 

87 

82 

79 

78 

19 

146 

146 

146 

146 

145 

141 

136 

129 

121 

112 

103 

95 

90 

86 

83 

20 

153 

1.-.:? 

153 

153 

152 

148 

144 

137 

129 

120 

111 

103 

97 

93 

90 

21 

158 

158 

158 

158 

157 

154 

150 

144 

136 

127 

118 

110 

104 

100 

97 

22 

163 

162 

162 

162 

161 

158 

154 

148 

140 

133 

124 

116 

HI 

106 

103 

23 

1G6 

165 

164 

163 

162 

100 

156 

150 

143 

136 

128 

121 

115 

112 

109 

24 

168 

166 

165 

164 

163 

160 

156 

151 

145 

138 

130 

124 

119 

116 

114 

25 

170 

167 

165 

161 

162 

160 

156 

151 

144 

138 

131 

125 

121 

119 

117 

26 

172 

168 

165 

163 

161 

158 

154 

149 

143 

136 

130 

124 

121 

119 

119 

27 

174 

169 

166 

163 

160 

157 

152 

147 

140 

134 

128 

123 

120 

119 

119 

28  ' 

176 

171 

167 

164 

160 

156 

151 

144 

138 

131 

125 

120 

117 

116 

117 

2'J 

179 

174 

169 

165 

161 

156 

150 

143 

136 

128 

122 

116 

113 

112 

114 

30 

183 

177 

172 

167 

162 

157 

150 

143 

135 

126 

118 

112 

109 

107 

109 

31 

187 

181 

176 

171 

166 

159 

152 

144 

134 

125 

116 

109 

104 

102 

103 

32 

190 

185 

181 

176 

170 

163 

155 

146 

1  35 

125 

114 

106 

100 

97 

97 

33 

194 

190 

186 

182 

176 

169 

160 

150 

138 

126 

114 

104 

96 

92 

91 

34 

198 

195 

192 

188 

183 

176 

166 

156 

143 

12!i 

115 

104 

94 

88 

86 

35 

201 

200 

198 

195 

190 

183 

174 

1G2 

149 

134 

119 

1  05 

94 

86 

82 

36 

204 

204 

203 

2H2 

197 

191 

182 

170 

156 

140 

124 

108 

95 

86 

80 

37 

205 

208 

208 

207 

204 

199 

191 

179 

164 

148 

131 

114 

99 

87 

80 

38 

205 

208 

211 

212 

211 

206 

199 

188 

174 

157 

139 

121 

105 

92 

83 

39 

204 

209 

213 

216 

216 

213 

207 

198 

184 

167 

149 

130 

113 

98 

88 

40 

201 

208 

214 

218 

220 

219 

215 

206 

194 

178 

160 

141 

"123 

107 

95 

41 

197 

205 

213 

219 

223 

224 

221 

215 

203 

189 

171 

153 

134 

118 

105 

42 

192 

202 

211 

219 

225 

228 

226 

222 

213 

200 

183 

165 

147 

130 

116 

43 

186 

197 

208 

217 

225 

230 

231 

229 

221 

211 

196 

178 

161 

143 

12!) 

44 

179 

192 

203 

214 

224 

231 

235 

234  | 

229 

221 

207 

191 

175 

158 

143 

45 

172 

185 

198 

210 

222 

231 

237 

239 

236 

230 

219 

204 

188 

172 

157 

46 

165 

178 

192 

206 

218 

230 

238 

242 

242 

238 

229 

216 

201 

186 

171 

47 

157 

171 

186 

200 

214 

227 

238 

245 

247 

245 

238 

227 

213 

199 

184 

48 

150 

163 

178 

194 

209 

224 

236 

246 

250 

250 

246 

237 

224 

211. 

196 

49 

142 

156 

171 

187 

204 

220 

234 

245 

252 

254 

252 

245 

234 

222 

208 

50 

134 

147 

162 

179 

197 

214 

230 

243 

252 

257 

256 

251 

242 

231 

218 

51 

136 

Kill 

154 

170 

189 

207 

225 

239 

250 

257 

259 

255 

248 

238 

226 

52 

117 

129 

144 

161 

180 

19!) 

218 

234    246 

25<) 

259 

258 

252 

243 

232 

53 

108 

119 

133 

150 

169 

189 

209 

226 

241 

252 

257 

258 

254 

247 

237 

54 

99 

109 

122 

138 

157 

178 

198 

217 

233 

245 

253 

256 

254 

249 

240 

55 

90 

98 

110 

125 

144 

164 

185 

205 

223 

237 

247 

251 

252 

248 

242 

56 

81 

87 

97 

111 

129 

149 

170 

191 

210 

226 

238 

245 

248 

246 

241 

57 

72 

76 

84 

96 

113 

133 

154 

175 

196 

213 

227 

236 

241 

242 

239 

58 

63 

64 

70. 

81 

96 

115 

136 

158 

179 

198 

214 

225 

233 

236 

835 

59 

55 

54 

57 

66 

79 

97 

117 

139 

161 

181 

199 

212 

222 

228 

230 

60 

4!) 

45 

4S 

51 

63 

79 

98 

119 

141 

163 

182 

198 

210 

218 

223 

The  perturbations  are  expressed  in  hundredths  of  a  second  of  arc. 


TAIILK    XXII. 


:*:* 


Perturbations  of  the  L«n->ititili-  /<//  th<-  l-'.nrih. 

llori/.tiiital  Argument  =  I. 

(.••umlaut  ailil.-il  l'..|tl.                    IVri.ul  ufAr.-.!..!.  MI  \  1  .  •_'  HI  iimls. 

.1 

.1 

,i 

.1             .1 

,1 

,l 

,i 

,1 

,i 

,1 

,i 

d 

,i 

4 

Ari  M 

120 

13* 

136 

111 

1*3 

100 

l««i 

IT« 

INI 

l»3 

300 

30* 

II« 

331 

333 

0 

188 

105 

801 

1    1 

911 

813 

-.'1  1 

914 

211 

1 

17.-. 

183 

iao 

193 

193 

197 

198 

901 

804 

919 

915 

816 

816 

•.'II 

2 

Ii,  -J        170 

177 

189 

1-:, 

1-7 

100 

103 

108 

813 

•-'17 

918 

916 

3 

llii        i.> 

166 

171 

171 

ITS 

l-l 

i-:, 

101 

107 

••  '1 

211 

216         -.'l:i 

•-'is 

4 

I3B 

nr 

156 

li,i 

164 

I6t) 

17'J 

177 

183 

u-o 

190 

•Jl  1 

818 

810 

5 

197 

136 

1  II 

ISO 

155 

158 

163 

168 

17:, 

I-:: 

199 

•Jin 

816 

810 

6 

III, 

197 

134 

141 

145 

140 

154 

ISO 

166 

176 

186 

1% 

211 

•ji- 

7            Iu7 

117 

1  25 

139 

137 

1  M 

145 

151 

158 

ton 

170 

I'.HI           '.Ml 

-.'II 

91? 

- 

BO 

100 

117 

I-JI 

138 

139 

137 

1  1-J 

150 

ISO 

171 

is:        l!Xi 

816 

D 

99 

101 

100 

116 

120 

184 

188 

134 

Ml 

161 

164 

177 

191 

•J  1  1 

814 

in 

BE 

96 

108 

108 

119 

116 

180 

1  25 

i:i:l 

149 

156 

17(1 

186 

813 

ii 

80 

06 

101 

106 

100 

113 

117 

194 

135 

1  1- 

164 

i-  i 

IIKJ 

•Jll 

19 

7(i 

-1 

00 

96 

90 

109 

106 

no 

117 

19} 

1  II 

157 

175 

109 

830 

13 

73 

BO 

91 

93 

95 

109 

100 

11!) 

134 

150 

160 

188 

14 

71 

77 

81 

85 

87 

89 

u 

05 

109 

118 

126 

149 

163 

184 

-.'  'l 

15 

71 

7.'. 

78 

81 

83 

84 

86 

89 

M 

lor, 

Illl 

136 

157 

17'J 

•.'ii 

16 

7',> 

75 

77 

79 

80 

80 

-.• 

-1 

89 

W 

Ill 

180 

150 

171 

I!i7 

17 

71 

76 

77 

78 

n 

77 

78 

7!l 

83 

99 

106 

1  22 

143 

167 

108 

1- 

78 

78 

7!) 

711 

78 

7li 

76 

76 

7!) 

96 

11.  -> 

136 

160 

l-:, 

10 

83 

83 

82 

81 

79 

77 

7:, 

74 

76 

82 

92 

108 

128 

161 

177 

90 

HO 

88 

86 

85 

82 

79 

71  i 

73 

74 

78 

87 

101 

119 

1  1-.' 

168 

81 

96 

94 

ga 

90 

87 

78 

71 

7:! 

7:. 

-J 

94 

HI 

189 

157 

89 

109 

101 

OB 

96 

99 

87 

82 

77 

74 

71 

78 

103 

189 

146 

23 

108 

107 

105 

103 

!«> 

93 

87 

81 

7.-, 

73 

75 

83 

95 

119 

134 

M 

114 

113 

112 

110 

105 

100 

99 

78 

74 

73 

78 

87 

102 

EU 

85 

118 

118 

117 

116 

111 

106 

98 

90 

82 

76 

79 

71 

HI 

98 

no 

96 

190 

121 

as 

QU 

117 

119 

104 

06 

86 

78 

73 

78 

71, 

99 

B7 

131 

123 

i-.v, 

ce 

rag 

117 

110 

101 

90 

-l 

71 

71 

79 

78 

90 

86 

1-J.i 

183 

BK 

127 

1  25 

121 

115 

106 

06 

-1 

76 

71 

(in 

73 

m 

as 

117 

121 

125 

127 

127 

IM 

118 

110 

99 

88 

78 

72 

68 

0:1 

7li 

30 

113 

nr 

122 

126 

127 

126 

121 

113 

IIKI 

92 

81 

74 

69 

87 

71 

M 

107 

112 

II- 

1X3 

MS 

185 

121 

115 

106 

96 

77 

70 

67 

69 

SB 

100 

KKi 

112 

118 

122 

183 

191 

117 

108 

09 

88 

72 

68 

68 

33 

94 

BO 

106 

113 

118 

121 

190 

117 

no 

101 

98 

83 

7(i 

71 

(ill 

34 

88 

99 

00 

107 

113 

117 

118 

117 

in 

104 

M 

87 

79 

74 

71 

35 

83 

86 

93 

101 

108 

113 

116 

116 

112 

106 

98 

91 

83 

77 

74 

•M 

7!) 

82 

88 

96 

103 

no 

114 

115 

113 

108 

109 

!)5 

87 

B8 

78 

37 

78 

7!) 

85 

99 

100 

107 

112 

II  1 

113 

110 

106 

90 

99 

86 

82 

38 

78 

70 

83 

90 

98 

106 

111 

114 

116 

119 

In- 

103 

06 

01 

86 

3!» 

82 

81 

84 

90 

98 

III.', 

111 

115 

117 

115 

Ill 

107 

100 

06 

91 

40 

88 

85 

87 

93 

100 

107 

113 

118 

no 

118 

115 

111 

111.-, 

100 

B6 

41 

96 

08 

93 

97 

104 

110 

117 

121 

193 

199 

II!) 

116 

100 

104 

90 

49 

106 

101 

101 

103 

109 

lir, 

121 

126 

127 

127 

124 

180 

114 

109 

104 

43 

118 

III 

110 

112 

116 

122 

187 

131 

133 

133 

rag 

196 

II!) 

114 

10!) 

44 

131 

123 

120 

mi 

MS 

130 

135 

rae 

139 

139 

136 

131 

186 

11:1 

114 

45 

144 

136 

132 

132 

134 

138 

142 

145 

146 

146 

142 

137 

131 

125 

120 

4(3 

158 

14!) 

144 

142 

144 

147 

151 

153 

154 

163 

140 

144 

138 

138 

196 

47 

171 

llil 

156 

153 

153 

156 

ISO 

169 

161 

160 

156 

151 

146 

13!) 

133 

48 

184 

173 

166 

163 

163 

164 

167 

168 

169 

167 

163 

158 

159 

146 

140 

49 

186 

184 

176 

172 

171 

172 

174 

17.', 

176 

174 

170 

res 

160 

i:,3 

148 

50 

2(T> 

104 

185 

181 

179 

179 

180 

181 

182 

180 

177 

ITS 

166 

160 

155 

51 

21:1 

202 

103 

188 

1-:, 

1  86 

186 

'187 

187 

186 

itg 

178 

179 

167 

169 

59 

883 

800 

wo 

194 

191 

190 

191 

192 

192 

191 

i  — 

I-l 

178 

173 

168 

53 

226 

215 

206 

200 

196 

1!).-, 

1  >:. 

1% 

196 

196 

109 

188' 

183 

178 

173 

:,i 

230 

221) 

211 

201 

1W 

l!«l 

19!) 

800 

180 

106 

192 

187 

189 

177 

55 

833 

224 

215 

20!) 

205 

202 

202 

m 

202 

201 

I!'- 

roe 

no 

l-l 

179 

56 

234 

226 

818 

213 

208 

206 

204 

805 

805 

203 

800 

107 

1!H 

IS, 

l-l 

57 

234 

227 

221 

215         211 

1    ' 

807 

808 

207 

805 

809 

i  e 

199 

186 

180 

:,- 

232 

227 

222 

•Jl-        214 

212 

210 

210 

800 

80S 

108 

199 

185 

17!) 

BO 

B86 

223 

219 

216 

214 

213 

212 

211 

•-"l 

198 

191 

1-1 

177 

GO 

224 

884 

222 

220 

218 

216 

815 

215 

819 

210 

198 

r.M 

1-:; 

171 

Add  147.64  to  Arg.  XI.  when  224'".7  is  subtra.  t.  ,1  iVuni  Arg.  I. 


TABLE  XXII. 


Perturbations  of  tin-  Longitude  bij  the  Earth. 

Horizontal  Argument  =  I. 

Constant  added  1;'.40.         Period  of  Argument  1.,  224J.7. 

d 

d 

did      d 

d 

d 

d 

d      d 

d 

rt 

d 

d 

d 

Arg.XI 

0 

| 

16 

!  24 

33 

4O 

48 

56 

01 

72 

80 

§§ 

96 

104 

112 

| 

60 

49 

45 

45 

51 

63 

.79 

98 

119 

141 

163 

182 

198 

210 

218 

223 

61 

44 

37 

85 

38 

47 

62 

79 

99 

122 

143 

164 

182 

196 

207 

214 

ea 

41 

31 

26 

27 

33 

41 

60 

80 

102 

121 

146 

164 

181 

194 

203 

G3 

41 

28 

21 

18 

21 

30 

44 

62 

83 

105 

127 

147 

164 

179 

191 

64 

43 

.28 

18 

12 

12 

18 

30 

45 

65 

86 

108 

128 

147 

164 

177 

65 

47 

31 

18 

10 

7 

10 

18 

32 

49 

69 

90 

111 

130 

147 

162 

66 

54 

36 

21 

11 

5 

4 

10 

21 

36 

54 

74 

94 

113 

131 

147 

67 

63 

44 

28 

15 

6 

3 

6 

14 

26 

42 

60 

79 

97 

U5 

131 

68 

73 

54 

37 

23 

12 

6 

5 

10 

20 

33 

48 

66 

83 

99 

115 

60 

85 

67 

49 

33 

21 

12 

9 

10 

16 

27 

40 

55 

70 

85 

100 

70 

97 

80 

63 

46 

32 

21 

15 

13 

16 

24 

34 

46 

60 

73 

87 

71 

110 

94 

78 

61 

45 

33 

24 

20 

20 

24 

31 

41 

52 

63 

75 

72 

1«3 

109 

93 

76 

60     47 

36 

29 

26 

27 

31 

38 

46 

55 

65 

73 

134 

123 

1(18 

92 

76 

62 

49 

40 

35 

33 

34 

38 

44 

51 

58 

74 

144 

135 

122 

107 

92 

77 

64 

53 

45 

41 

40 

41 

44 

48 

54 

75 

153 

145 

135    122 

107 

92 

78 

66 

57 

51 

47 

46 

47 

49 

52 

76 

160 

155 

146    134 

121 

107 

93 

80 

69 

62 

56 

53 

52 

52 

53 

77 

165 

162 

155    145 

133 

120 

106 

93 

82 

73 

66 

62 

59 

57 

56 

78 

169 

167 

162    153 

144 

131 

118 

106 

94 

85 

77 

71 

67 

64 

61 

79 

171 

170 

167 

160 

152 

141 

129 

117 

106 

96 

88 

81 

76 

71 

67 

80 

172 

172 

170 

165 

158 

149 

138 

127 

116 

107 

99 

91 

85 

80 

75 

81 

172 

172 

171 

168 

163 

155 

146 

136 

126 

117 

108 

101 

95 

89 

83 

82 

171 

172 

171 

169 

166 

160 

152 

144 

134 

126 

118 

110 

104 

97 

90 

83 

170 

171 

171 

170 

167 

163 

157 

150 

142 

134 

126 

119 

112 

105 

98 

84 

169 

169 

169 

169 

168 

165 

161 

155 

148 

141 

134 

126 

120 

112 

105 

85 

168 

168 

168 

168 

168 

166 

163 

158 

153 

147 

140 

133 

126 

119 

111 

86 

108 

166 

166 

167 

167 

167 

165 

161 

157 

152 

145 

139 

132 

124 

116 

87 

167 

165 

164 

166 

166 

167 

166 

163 

160 

156 

150 

143 

136 

12!) 

120 

88 

167 

164 

163 

165 

164 

166 

166 

165 

163 

159 

153 

147 

140 

133 

123 

8!) 

167 

163 

161 

162 

163 

165 

166 

166 

164 

161 

156 

151 

144 

136 

126 

90 

167 

162 

160  i   160 

162 

163 

165 

166 

165 

163 

159 

154 

147 

139 

129 

!H 

168 

162 

159  I   158 

159 

161 

164 

165 

165 

164 

161 

156 

150 

142 

132 

9SJ 

168 

161 

157    156 

157 

159 

162 

164 

165 

165 

162 

158 

153 

145 

136 

93 

168 

160 

156    153 

154 

156 

159 

162 

164 

165 

163 

161 

156 

148 

139 

94 

168 

16i) 

154 

151 

151 

152 

156 

159 

162 

164 

164 

163 

158 

152 

144 

95 

169 

159 

153 

149 

148 

149 

152 

156 

160 

163 

165 

164 

162 

157 

149 

96 

169 

159 

152 

147 

145 

146 

149 

153 

158 

162 

165 

166 

165 

161 

154 

97 

170 

159 

151 

145 

143 

143 

145 

150 

155 

161 

165 

168 

168 

166 

160 

08 

171 

160 

151 

145 

141 

140 

143 

147 

153 

159 

165 

169 

171 

171 

167 

9!) 

172 

162 

152 

145 

140 

139 

140 

145 

151 

158 

164 

171 

174 

175 

174 

100 

171 

164 

154 

146 

141 

138 

139 

143 

150 

157 

165 

172 

177 

180 

180 

101 

176 

167 

158 

149 

143 

140 

140 

143 

149 

157 

165 

173 

180 

184 

186 

102 

179 

171 

162 

163 

146 

142 

141 

144 

149 

157 

166 

175 

183 

189 

191 

103 

182 

175 

166 

158 

151 

146 

144 

146 

151 

158 

167 

176 

185 

192 

196 

104 

184 

179 

171 

163 

156 

151 

149 

149 

153 

160 

169 

178 

187 

195 

200 

105 

187 

183 

177 

170 

163 

157 

154 

154 

157 

163 

171 

180 

189 

198 

203 

106 

188 

186 

181 

176 

16!) 

164 

160 

159 

161 

166 

173 

182 

191 

200 

236 

107 

188 

188 

185 

181 

176 

170 

167 

165 

166 

16!) 

175 

184 

193 

201 

208 

108 

186 

18!) 

188 

185 

•  181 

176 

173 

170 

170 

173 

178 

186 

194 

203 

210 

109 

182 

187 

189 

188 

185 

181 

178 

175 

175 

176 

180 

187 

195 

203 

211 

110 

177 

184 

188 

188 

187  |   184 

181 

179 

178 

179 

182 

188 

195 

204 

212 

111 

170 

178 

183 

186 

186 

185 

183 

181 

180 

180 

183 

189 

195 

203 

211 

112 

161 

171 

177 

182 

183 

184 

182 

181 

180 

181 

183 

188 

194 

202 

210 

113 

150 

161 

168 

171 

177    179 

179 

17!) 

179 

179 

181 

186 

192 

201 

209 

114 

138 

149 

157 

164 

169 

172. 

174 

175 

175 

176 

178 

183 

189 

198 

206 

115 

125 

136 

145 

153 

158    163 

166 

168 

169 

171 

174 

179 

185 

193 

203 

116 

112 

122 

131 

140 

146    152 

156 

159 

162 

164 

168 

173 

•  179 

188 

198 

117 

99 

108 

117 

125 

132  !   139 

144 

149 

158 

156 

160. 

165 

172 

181 

192 

118 

87 

95 

102 

110 

118 

125 

132 

137 

142 

146 

151 

157 

164 

174 

184 

119 

76 

82 

89 

96 

104 

111 

11!) 

125 

131 

136 

Ml 

148 

155 

164 

175 

120 

67 

71 

77 

83 

90 

98 

106 

113 

119 

125 

131 

138 

145 

154 

165 

The  perturbations  arc  expressed  in  Imndredths  of  a  second  of  arc, 


TABLE  XXII. 


/'  rturbiilinnx  .//"//»•  Lmigituih-  Inj  tlir  Kartli. 

Horizontal  Argument  =  I. 

r.m-t:nit  aild..,l  1"  1  >                       IVn-d  of  Argument  XI  ,2-10  units. 

d 

d 

d 

d 

.) 

,1 

,1 

,l 

d 

d             d 

d 

d 

,1 

.1 

Arg.  XI 

iaa 

i:tO 

111 

i.ia 

160 

1CN 

176 

INI 

aoo 

aoM 

a  10 

aai 

a.ta 

60 

994 

221 

999 

99  ' 

918 

216 

215 

916 

913 

210 

205 

198 

191 

183 

174 

til 

21  a 

910 

21!'         21!) 

21-         21- 

217 

917 

215 

211 

109 

100 

l-l 

171 

69 

900 

913 

2  Hi         217 

818 

818 

918 

918 

217 

213 

2,  i7 

100 

ISO 

170 

63 

199 

2  .0 

210            211 

816 

818 

819 

918 

915 

2H1 

1!H 

l-o 

KJ8 

01 

188 

106 

803 

813 

816 

21- 

990 

819 

916 

211 

903 

193 

180 

168 

05 

175 

1-5 

194 

201 

212 

216 

220 

220 

918 

213 

205 

100 

183 

169 

66 

KM 

172 

l-:i 

109 

200 

813 

918 

22  ' 

919 

215 

2os 

108 

186 

172 

67 

115 

158 

181 

191 

200 

215 

918 

219 

217 

211 

202 

100 

177 

68' 

130 

1  i:: 

156 

168 

180 

101 

901 

210 

210 

9111 

217 

21  1 

106 

1-2 

69 

115 

12- 

1  12 

155  • 

168 

l-l 

IBS 

904 

919 

217 

919 

217 

210 

•Jil 

1-:' 

70 

100 

114 

127 

1  II 

1  56 

16!) 

l-l 

106 

215 

219 

21:1 

214 

206 

1!  '5 

71 

-7 

100 

113 

127 

1  12 

157 

173 

188 

2  H 

211 

21- 

22  I 

918 

911 

909 

72 

76 

87 

100 

III 

189 

115 

l',2 

17- 

194 

215 

980 

890 

916 

20!) 

73 

67 

77 

88 

101 

116 

133 

151 

1  .- 

1-5 

200 

211 

910 

221 

220 

214 

74 

61 

68 

78 

90 

121 

|:l  ' 

1    - 

170 

193 

207 

216 

221 

222 

218 

75 

57 

63 

71 

81 

90 

110 

12- 

1  1- 

107 

185 

201 

212 

219 

222 

220 

76 

55 

59 

65 

74 

86 

101 

118 

137 

157 

177 

II 

207 

216 

2-20 

221 

77 

56 

58 

63 

69 

7!) 

93 

100 

138 

148 

107 

185 

200 

211 

217 

919 

7- 

60 

60 

62 

67 

75 

87 

109 

1  i'.i 

138 

158 

177 

109 

904 

212 

215 

n 

65 

63 

63 

66 

72 

81 

111 

129 

14!) 

167 

tea 

1% 

205 

210 

80 

70 

67 

65 

66 

70 

77 

103 

120 

139 

157 

17:t 

1-7 

197 

203 

81 

77 

73 

69 

67 

(i!) 

75 

84 

112 

189 

147 

163 

177 

l-s 

194 

82 

84 

78 

73 

69 

BO 

72 

7!) 

90 

104 

180 

137 

152 

166 

177 

1^5 

83 

90 

-1 

77 

72 

09 

70 

75 

-1 

.   HI 

126 

III 

156 

107 

175 

84 

97 

89 

81 

74 

70 

68 

71 

77 

88 

101 

116 

130 

1  15 

156 

104 

83 

102 

93 

84 

76 

70 

66 

07 

72 

80 

92 

106 

119 

134 

115 

154 

H6 

106 

97 

86 

77 

70 

64 

03 

Mi 

73 

'Kj 

100 

123 

134 

1  13 

>7 

110 

100 

H8 

78 

(i'.i 

62 

59 

60 

65 

71 

86 

119 

123 

133 

88 

113 

102 

90 

78 

K 

60 

55 

51 

58 

05 

71  i 

88 

Ml 

113 

122 

89 

116 

104 

79 

67 

58 

52 

49 

51 

57 

67 

78 

01 

102 

112 

90 

118 

106 

93 

80 

67 

56 

49 

45 

45 

50 

58 

68 

81 

92 

102 

121 

100 

05 

81 

67 

56 

46 

42 

40 

43 

51 

60 

71 

82 

92 

124 

112 

98 

83 

69 

56 

45 

39 

30 

38 

44 

52 

03 

73 

03 

128 

110 

102 

87 

71 

58 

46 

38 

34 

33 

38 

45 

55 

00 

71 

M 

133 

121 

107 

91 

76 

61 

48 

38 

33 

31 

34 

39 

48 

S3 

(>0 

95 

13!) 

127 

113 

97 

81 

66 

52 

41 

33 

30 

31 

35 

12 

50 

58 

96 

146 

134 

121 

105 

-•i 

73 

45 

36 

31 

30 

32 

88 

15 

11 

97 

153 

142 

129 

114 

97 

81 

65 

51 

41 

34 

31 

31 

35 

40 

46 

98 

161 

151 

139 

121 

107 

91 

74 

59 

47 

89 

34 

32 

35 

38 

43 

99 

16!) 

160 

14!) 

134 

118 

101 

84 

68 

55 

15 

3!) 

35 

36 

38 

42 

100 

177 

169 

159 

145 

129 

113 

00 

78 

64 

53 

45 

40 

40 

40 

42 

101 

184 

178 

169 

156 

141 

124 

90 

75 

61 

51 

47 

45 

44 

45 

102 

191 

187 

178 

100 

159 

136 

11!) 

101 

B6 

73 

63 

55 

52 

50 

11 

103 

197 

104 

187 

176 

163 

117 

130 

113 

97 

84 

73 

05 

01 

58 

.,.- 

104 

203 

201 

1  :'5 

185 

173 

158 

141 

185 

109 

90 

84 

70 

71 

68 

67 

105 

207 

206 

202 

193 

l-l 

107 

152 

136 

120 

106 

96 

87 

-2 

7!) 

7- 

106 

210 

211 

207 

200 

189 

176 

102 

115 

131 

118 

107 

90 

!'l 

91 

80 

107 
108 
109 

214 
216 

217 

215 
218 
993 

819 

217 

220 

206 
211 
216 

107 

203 
209 

184 
192 
198 

171 
186 

155 
164 
173 

Ml 
151 
160 

I3U 
148 

11- 
12!) 
139 

111 
122 
132 

106 
117 

12- 

too 

114 

125 

113 
121 

110 
III 
112 
113 
114 

218 
218 
218 
217 
815 

222 
223 
994 
824 

223 

223 

225 
227 
888 
889 

220 
223 
226 
899 

231 

214 
218 
223 
227 
230 

205 
210 
815 

2-20 
225 

193 
200 
206 
212 
217 

180 

188 
195 

201 

207 

168 
176 

183 

I'.H) 
1% 

157 
165 

173 

•     1  96 

148 

1.56 
164 
170 
176 

112 
150 
157 
103 
169 

137 
146 
153 
159 
164 

136 

I  II 

151 
157 

11,1 

M 
143 

151 

116 

161 

115 
116 
117 
118 
119 
190 

213 

213 
1% 
188 

178 

221 
218 
214 

2.)0 
101 

22H 
227 
824 
21!) 
212 
204 

232 
232 
230 
227 
222 
215 

232 
934 

234 
838 

22:) 
224 

22!) 
833 

233 
834 

232 

22- 

222 
226 
22!) 
231 
831 
230 

212 
217 
221 
294 

226 
227 

202 

212 
216 
219 
990 

ini 
UK 

809 

212 

1-2 
1-7 
101 
105 
191) 
202 

171 

17- 
I-J 
1-5 
1-:' 

109 

168 
172 
175 
177 
180 
183 

166 

170 
172 
171 

171, 

163 
169 

107 

IW 

160 

I7o 

10  V 


Add  147.64  to  Arg.  XI.  when  224''.7  is  subtracted  from  Arg.  I. 


TABLE   XX11. 


Perturbations  oft/if  Longitude  by  the  Earth. 

Horizontal  Argument  =  I. 

Constant  added  1''.40.         Period  of  Argument  I.,  224''  .7. 

d 

d 

d 

d 

d 

d 

d  :    d 

d 

d 

d 

d 

d 

d 

d 

Arg.XI 

0 

8 

1G 

24 

32 

40 

48 

56 

61 

72 

80 

88 

96 

1O4 

112 

120 

67 

71 

77 

83 

00 

98 

106 

113 

119 

125 

131 

138 

145 

154 

165 

181 

50 

62 

66 

71 

78 

86 

93 

101 

108 

111 

121 

127 

134 

143 

154 

122 

53 

55 

57 

62 

67 

75 

83 

90 

98 

"  104 

110 

117 

124 

132 

142 

123 

53 

51 

51 

54 

59 

65 

73 

80 

88 

94 

101 

107 

113 

121 

131 

124 

48 

47 

47 

49 

53 

58 

65 

72 

80 

86 

92 

99 

104 

111 

119 

135 

48 

46 

45 

46 

48 

53 

59 

66 

73 

79 

85 

91 

96 

101 

108 

186 

49 

46 

45 

44 

46 

49 

55 

61 

68 

74 

80 

84 

89 

93 

99 

127 

52 

49 

46 

45 

4r> 

48 

52 

58 

65 

70 

76 

80 

83 

87 

91 

128 

56 

52 

49 

46 

46 

47 

51 

57 

62 

68 

73 

77 

80 

82 

86 

129 

60 

56 

52 

49 

47 

48 

51 

56 

62 

67 

72 

76 

78 

80 

82 

ISO 

05 

61 

56 

52 

50 

49 

52 

56 

61 

67 

72 

76 

79 

80 

81 

181 

70 

66 

61 

56 

53 

51 

53 

57 

62 

68 

74 

78 

80 

82 

83 

132 

76 

71 

65 

60 

56 

54 

55 

58 

63 

69 

75 

80 

83 

85 

86 

133 

82 

76 

70 

64 

59 

56 

56 

59 

64 

70 

77 

83 

87 

90 

91 

134 

89 

82 

75 

68 

62 

58 

58 

60 

65 

72 

79 

86 

92 

95 

97 

135 

96 

88 

80 

73 

66 

61 

60 

62 

66 

73 

81 

90 

96 

101 

104 

136 

103. 

!I5 

86 

77 

70 

64 

62 

63 

67 

75 

83 

92 

101 

107 

111 

137 

112 

||  :! 

93 

83 

74 

68 

65 

65 

69 

76 

85 

95 

104 

112 

117 

138 

121 

Ill    100 

90 

80 

72 

68 

67 

70 

77 

86 

97 

107 

116 

123 

139 

131 

12!    109 

97 

86 

77 

72 

70 

72 

78 

87 

98 

109 

119 

127 

140 

111 

m    118 

106 

94 

84 

76 

73 

74 

79 

87 

98 

110 

121 

130 

141 

152 

141 

128 

115 

102 

91 

82 

78 

76 

80 

87 

98 

109 

121 

131 

142 

•163 

151 

138 

125 

111 

99 

89 

83 

80 

81 

87 

97 

108 

119 

130 

143 

173 

162 

149 

136 

12,1 

108 

96 

88 

84 

83 

88 

96 

106 

117 

I2H 

144 

183 

173 

161 

147 

132 

117 

104 

94 

88 

86 

88 

94 

103 

114 

125 

145 

193 

183 

171 

158 

142 

127 

113 

101 

93 

88 

89 

93 

100 

110 

121 

146 

201 

193 

181 

168 

153 

137 

122 

109 

98 

92 

90 

92 

98 

106 

116 

147 

208 

201 

190 

178 

163 

147 

130 

117 

104 

95 

91 

91 

95 

102 

111 

148 

213 

207 

198 

186 

172 

156 

139 

124 

110 

100 

94 

92 

93 

99 

107 

14!) 

217 

212 

205 

194 

181) 

164 

147 

131 

116 

105 

97 

92 

93 

96 

103 

150 

219 

216 

210 

200 

187 

172 

155 

138 

123 

110 

100 

94 

92 

94 

100 

151 

219 

218 

214 

205 

194 

179 

162 

146 

130 

115 

104 

97 

94 

94 

98 

153 

218 

219 

216 

209 

199 

185 

169 

1  53 

136 

121 

109 

100 

96 

94 

97 

153 

217 

219 

218 

213 

204 

191 

176 

159 

143 

128 

115 

105 

99 

96 

97 

154 

214 

218 

219 

216 

208 

197 

183 

166 

151 

135 

122 

111 

103 

99 

99 

155 

211 

217 

220 

218 

212 

202 

189 

174 

158 

143 

129 

118 

109 

103 

102 

156 

208 

215 

220 

228 

217 

898 

196 

182 

167 

152 

138 

125 

116 

109 

106 

157 

204 

214 

221 

223 

221 

215 

2114 

I'll 

177 

161 

147 

134 

124 

116 

111 

158 

200 

212 

221 

226 

226 

221 

212 

200 

187 

172 

158 

144 

133 

123 

117 

159 

197 

211 

222 

229 

231 

228 

221 

210 

198 

183 

16!) 

155 

143 

132 

125 

160 

193 

209 

222 

232 

236 

236 

230 

221 

209 

196 

182 

167 

154 

142 

133 

161 

189 

207 

223 

235 

242 

243 

240 

232 

221 

208 

194 

180 

166 

153 

143 

162 

185 

204 

223 

237 

246 

250 

249 

242 

233 

221 

207 

193 

179 

165 

154 

163 

179 

201 

221 

238 

250 

256 

257 

253 

245 

234 

221 

206 

192 

178 

165 

164 

17:i 

197 

219 

238 

252 

261 

264 

262 

255 

245 

233 

219 

205 

191 

178 

165 

167 

191 

215 

236 

252 

263 

269 

269 

264 

256 

245 

232 

219 

204 

191 

166 

159 

184 

209 

232 

250 

264 

272 

274 

271 

265 

256 

244 

231 

218 

204 

167 

150 

176 

201 

225 

246 

261 

271 

276 

276 

272 

264 

254 

243 

230 

217 

168 

141 

166 

192 

217 

239 

256 

269 

276 

278 

276 

270 

263 

953 

242 

230 

169 

131 

155 

181 

206 

229 

249 

263 

272 

277 

277 

274 

269 

261 

252 

242 

170 

120 

144 

168 

194 

217 

238 

254 

266 

272 

276 

275 

272 

267 

260 

252 

171 

110 

132 

155 

180 

204 

B25 

243 

256 

265 

271 

273 

272 

270 

266 

260 

172 

100 

119 

141 

165 

189 

210 

229 

244 

255 

263 

267 

270 

270 

968 

265 

173 

1)1 

108 

128 

150 

173 

194 

213 

230 

242 

252 

259 

264 

267 

268 

268 

174 

84 

97 

115 

135 

1ST1 

178 

197 

214 

228 

239 

248 

255 

261 

265 

267 

175 

77 

88 

103 

121 

141 

161 

180 

197 

212 

224 

235 

244 

S53 

258 

263 

176 

72 

80 

93 

109 

127 

145 

163 

180 

195 

208 

220 

230 

239 

248 

256 

177 

69 

75 

84 

98 

114 

130 

147 

163 

177 

191 

203 

214 

225 

235 

245 

178 

67 

71 

78 

89 

103 

117 

132 

147 

169 

173 

185 

197 

2J9 

220 

231 

179 

68 

69 

74 

82 

94 

106 

119 

132 

144 

156 

167 

179 

191 

203 

215 

180 

69 

68 

71 

78 

87 

97 

108 

119 

129 

140 

150 

161 

172 

185 

fee 

The  perturbations  are  expressed  in  hundredths  of  a  second  of  arc. 


TABLE   XXII. 


Perturbations  of  the  L           •  ,-th. 

lli'i'i/uiitul  Ar^iiiiii-iit  =  I. 
r,,u..i;,i>t  addi-d  I'.ll        IVriud  ..fArf-iim-m  XI  ,  210  units. 

Ar^.M 

<\ 
120 

,l 

a 

i  ;<; 

111 

192 

•100 

,1 
10M 

,1 

,1 
INI 

,1 

200 

cl 

20* 

210 

22  i' 

»».' 

190 

17- 

191 

904 

215 

22  1 

898 

212 

199 

1-:; 

I76 

170 

121 

167 

180 

103 

916 

893 

221 

213 

106 

l-i, 

1  7'.  I 

173 

122 

155 

168 

189 

105 

916 

991 

22  1 

910 

21  1 

198 

1  89 

176 

193 

1  12 

155 

160 

1-:: 

913 

916 

217 

913 

2  17 

193 

Mi 

l-n 

121 

12:1    111 

166 

169 

l-:i 

196 

210 

212 

211 

196 

I  no 

l-l 

195 

117 

198 

1  II 

156 

170 

I-:; 

I'.il 

207 

2i- 

2.17 

lOt) 

I'H 

tan 

I2li 

106 

116 

198 

1  12 

156 

170 

189 

199 

199 

2iil 

901 

IU8 

in 

127 

'.17 

105 

III, 

190 

112 

17 

170 

1-2 

IU1 

1  'i7 

2  13 

2  '1 

r.ni 

I2S 

96 

105 

117 

130 

Ml 

158 

171 

1-2 

191 

197 

201 

903 

2  13 

12!) 

* 

90 

:i7 

107 

119 

133 

Mi, 

11,1 

173 

l-l 

199 

108 

109    205 

2  Hi 

i:;  i 

83 

96 

99 

100 

110 

193 

137 

151 

164 

17(i 

186 

194    200 

2  I5 

2i- 

131 

-:> 

85 

99 

95 

|0| 

115 

12- 

1  12 

i.-,-, 

l<,  - 

179 

L-.i    l'.<7 

2  'I 

909 

132 

-7 

89 

93 

100 

no 

191 

134 

117 

li,l 

173 

l-l    193 

903 

133 

!U 

91 

!i| 

!I4 

99 

106 

116 

127 

1  |:l 

153 

166 

177    I-- 

ION 

906 

134 

117 

(17 

96 

97 

100 

105 

113 

122 

134 

in, 

159 

171 

1-2 

193 

903 

135 

105 

104 

103 

101 

103 

106 

ill 

11!) 

199 

i  r> 

159 

164 

176 

188 

199 

136 

112 

112 

110 

108 

107 

108 

112 

117 

125 

134 

145 

157 

169 

l-l 

IDS 

137 

121 

190 

118 

115 

113 

119 

113 

116 

122 

130 

139 

150 

169 

175 

187 

138 

196 

127 

196 

12:1 

119 

116 

116 

111 

121 

121, 

133 

1  II 

155 

Ki7 

1-  , 

139 

133 

134 

133 

130 

125 

121 

119 

117 

118 

122 

198 

137 

117 

160 

173 

Mi 

136 

139 

139 

135 

131 

126 

122 

118 

117 

119 

193 

131 

140 

152 

166 

141 

138 

142 

113 

140 

135 

130 

124 

119 

116 

116 

119 

125 

133 

144 

168 

112 

138 

144 

145 

143 

139 

133 

126 

120 

116 

ill 

115 

119 

196 

136 

ii' 

143 

137 

143 

146 

145 

141 

134 

12- 

12:1 

11.-, 

ill 

III! 

111 

in 

128 

Ml 

III 

134 

141 

145 

145 

112 

138 

128 

121 

Ill 

lll'.l 

106 

108 

111 

190 

132 

145 

130 

137 

142 

143 

141 

138 

12- 

120 

113 

1'  ,, 

109 

102 

104 

111 

122 

III, 

195 

133 

13!) 

141 

13!) 

135 

12- 

119 

111 

|0| 

08 

96 

97 

103 

112 

147 

190 

198 

136 

137 

137 

133 

127 

118 

no 

101 

94 

91 

89 

93 

101 

1  1- 

115 

193 

130 

134 

134 

131 

126 

117 

109 

DO 

in 

96 

99 

84 

91 

14!) 

110 

118 

125 

130 

132 

130 

124 

117 

108 

97 

88 

81 

75 

75 

79 

150 

106 

111 

121 

126 

129 

128 

123 

116 

107 

96 

a-> 

76 

(i:i 

67 

68 

51 

103 

no 

117 

123 

126 

126 

123 

116 

107 

84 

73 

61 

59 

57 

52 

101 

107 

114 

190 

121 

125 

122 

117 

108 

96 

83 

71 

50 

59 

1- 

53 

too 

106 

112 

118 

193 

194 

199 

117 

109 

97 

83 

70 

57 

47 

40 

54 

101 

105 

111 

117 

121 

194 

123 

118 

110 

99 

85 

71 

56 

43 

34 

55 

102 

105 

110 

116 

121 

12:i 

123 

120 

113 

102 

88 

73 

56 

42 

30 

105 

107 

111 

115 

120 

123 

121 

121 

115 

106 

99 

76 

59 

43 

99 

57 

109 

109 

112 

116 

120 

123 

121 

123 

11- 

100 

96 

81 

64 

46 

31 

58 

113 

112 

113 

117 

190 

123 

125 

1  25 

121 

114 

102 

-7 

70 

59 

35 

159 

119 

116 

116 

118 

120 

123 

126 

126 

121 

118 

108 

95 

78 

i,  i 

42 

160 

126 

122 

119 

119 

121 

194 

126 

128 

126 

199 

lit 

103 

88 

70 

52 

161 

134 

198 

124 

122 

193 

125 

127 

I2!l 

12!) 

127 

121 

111 

98 

-2 

III 

169 

14  I 

135 

130 

126 

125 

196 

12- 

130 

132 

131 

127 

190 

108 

:n 

77 

163 

154 

144 

136 

131 

12!) 

12- 

130 

132 

134 

135 

133 

12- 

1  l!l 

107 

91 

164 

165 

154 

145 

138 

133 

132 

139 

134 

137 

139 

130 

136 

12!) 

119 

in:, 

165 

178 

165 

155 

146 

140 

137 

136 

137 

140 

142 

Ml 

143 

138 

131 

119 

166 

100 

178 

166 

155 

148 

143 

Ml 

Ml 

113 

146 

148 

149 

117 

141 

131 

167 

204 

101 

17- 

167 

158 

151 

147 

145 

147 

14!) 

159 

155 

154 

150 

1  12 

168 

218 

205 

192 

179 

169 

160 

154 

151 

151 

153 

166 

I.V.I 

159 

157 

169 

231 

218 

206 

192 

181 

171 

163 

158 

166 

157 

159 

162 

163 

163 

15!) 

170 

242 

939 

220 

206 

194 

183 

173 

166 

162 

161 

162 

166 

166 

Ki7 

165 

171 

252 

944 

233 

220 

2,17 

r  5 

184 

175 

Hi!) 

166 

166 

11,7 

!(,- 

170 

160 

172 

969 

254 

244 

233 

220 

207 

196 

184 

176 

171 

16!) 

169 

170 

171 

171 

173 

966 

260 

254 

244 

839 

919 

206 

194 

l-l 

176 

172 

171 

170 

171 

172 

174 

268 

266 

261 

253 

243 

230 

216 

203 

191 

1-2 

175 

172 

171 

171 

172 

175 

267 

267 

265 

260 

251 

226 

212 

roe 

187 

I7'i 

171 

171 

170 

171 

176 

969 

966 

266 

263 

257 

246 

233 

21!) 

1  ". 

1-2 

175 

171 

17'l 

Mil 

177 

254 

260 

264 

263 

25!) 

951 

939 

226 

211 

106 

l-i, 

177 

171 

li,  ' 

168 

949 

251 

257 

260 

258 

253 

213 

230 

216 

189 

179 

172 

168 

11,7 

t!7  ' 
i 

998 

939 

248 

254 

255 

252 

211 

233 

219 

906 

l-l 

173 

I6H 

165 

189 

211 

2-21 

2;t6 

244 

248 

21- 

213 

233 

207 

196 

1-3 

171 

167 

H,  1 

Add  147.64  to  Arg.  XI.  wln'ii  22I''.7  in  nublracted  from  Arg.  I. 


TABLE  XXII. 


Perturbations  of  the  Longitude  by  the  Earth. 

Horizontal  Argument  =  I. 

Constant  added  1".40.           Period  of  Argument  I.  224'].7. 

Arg.  XI 

d 

o 

ii 
8 

i 
16 

|  24 

32 

40 

d 

48 

5« 

,1 
<»1 

tl 
72 

d 

SO 

d 
88 

d 

96 

a 
1O4 

t 
112 

180 

CO 

68 

71 

78 

87 

97 

108 

110 

129 

140 

150 

161 

172 

185 

198 

181 

72 

70 

71 

75 

82 

00 

09 

107 

116 

125 

133 

143 

154 

166 

170 

182 

75 

72 

72 

74 

70 

85 

91 

08 

105 

111 

118 

126 

136 

147 

160 

183 

70 

75 

74 

75 

78 

82 

86 

90 

95 

09 

104 

110 

119 

129 

141 

184 

83 

70 

77 

77 

78 

80 

82 

85 

87 

89 

93 

06 

103 

112 

123 

is:; 

87 

83 

80 

70 

79 

80 

80 

81 

81 

82 

83 

85 

89 

07 

107 

186 

92 

87 

84 

82 

81 

80 

80 

78 

77 

76 

75 

/o 

78 

83 

93 

187 

96 

92 

88 

86 

84 

82 

80 

77 

75 

72 

69 

63 

69 

73 

81 

188 

101 

06 

03 

89 

87 

85 

82 

78 

74 

70 

66 

63 

62 

64 

71 

180 

105 

100 

97 

94 

01 

88 

85 

80 

75 

6!) 

64 

60 

57 

58 

63 

100 

110 

105 

101 

08 

05 

02 

88 

83 

77 

71 

64 

58 

55 

54 

58 

191 

115 

no 

106 

103 

100 

06 

02 

87 

81 

74 

66 

50 

54 

52 

54 

102 

121 

116 

112 

108 

.105 

102 

97 

92 

85 

78 

70 

62 

56 

52 

52 

193 

127 

122 

117 

114 

111 

108 

104 

98 

01 

83- 

74 

66 

58 

54 

52 

194 

133 

129 

124 

121 

118 

114 

111 

105 

08 

90 

81 

71 

62 

56 

53 

105 

140 

136 

131 

123 

125 

122 

118 

113 

106 

98 

83 

77 

67 

60 

55 

106 

147 

143 

138 

136 

133 

130 

127 

121 

115 

106 

96 

84 

73 

64 

58 

197 

154 

150 

146 

143 

140 

138 

135 

131 

124 

115 

104 

02 

80 

60 

61 

1!)8 

161 

157 

153 

150 

148 

146 

144 

140 

134 

124 

113 

100 

87 

75 

65 

199 

168 

164 

160 

157 

156 

154 

.152 

149 

143 

134 

122 

100 

94 

81 

60 

200 

173 

170 

166 

164 

163 

161 

160 

157 

151 

143 

131 

117 

102 

87 

74 

201 

178 

174 

171 

169 

168 

167 

167 

164 

159 

151 

139 

125 

109 

04 

70 

202 

182 

178 

174 

172 

172 

172 

72 

70 

166 

158 

147 

133 

117 

100 

84 

203 

184 

180 

176 

174 

174 

174 

75 

74 

171 

1G4 

154 

140 

124 

107 

00 

204 

185 

180 

176 

174 

174 

175 

76 

76 

174 

168 

159 

146 

130 

113 

06 

905 

184 

180 

175 

173 

173 

173 

75 

76 

175 

171 

162 

151 

136 

119 

101 

206 

184 

178 

173 

170 

169 

170 

72 

74 

174 

171 

165 

155 

141 

124 

107 

207 

182 

175 

170 

165 

164 

165 

167 

70 

171 

170 

165 

157 

144 

129 

112 

208 

181 

173 

166 

160 

158 

160 

162 

165 

167 

167 

164 

157 

147 

133 

117 

209 

170 

170 

162 

156 

153 

153 

155 

159 

162 

164 

162 

157 

148 

136 

120 

210 

178 

168 

150 

152 

148 

147 

149 

153 

156 

150 

159 

156 

143 

137 

124 

211 

170 

167 

157 

149 

144 

142 

142 

146 

150 

154 

155 

153 

148 

138 

126 

212 

180 

167 

156 

146 

140 

137 

137 

141 

145 

148 

151 

150 

146 

138 

127 

213 

182 

169 

157 

146 

130 

135 

134 

136 

140 

143 

147 

148 

144 

133 

128 

214 

186 

172 

IG;) 

148 

130 

134 

132 

133 

137 

141 

144 

145 

143 

137 

123 

215 

190 

177 

164 

152 

M2 

136 

133 

133 

135 

139 

142 

143 

141 

136 

123 

216 

106 

183 

170 

157 

147 

130 

135 

134 

136 

138 

141 

142 

141 

136 

120 

217 

202 

190 

177 

164 

153 

145 

140 

138 

138 

140 

142 

143 

141 

137 

129 

218 

207 

107 

185 

172 

161 

152 

146 

143 

143 

143 

145 

145 

143 

139 

131 

210 

213 

204 

193 

181 

170 

163 

151 

150 

14!) 

148 

149 

149 

146 

'142 

135 

220 

217 

210 

20!) 

180 

179 

169 

162 

158 

156 

155 

155 

154 

151 

147 

139 

2-31 

220 

215 

207 

197 

187 

178 

171 

166 

164 

162 

162 

161 

158 

153 

146 

222 

222 

210 

212 

21)4 

105 

186 

180 

175 

172 

171 

170 

160 

166 

161 

154 

223 

221 

220 

216 

209 

201 

193 

187 

183 

181 

179. 

179 

178 

175 

171 

163 

224 

219 

220 

217 

212 

205 

109 

194 

190 

188 

187 

187 

187 

185 

181 

174 

225 

215 

218 

217 

213 

208 

202 

198 

195 

104 

104 

105 

106 

105 

192 

186 

226 

210 

214 

214 

211 

238 

204 

201 

1  00 

109 

200 

202 

204 

204 

232 

103 

227 

202 

208 

209 

208 

206 

203 

201 

201 

202 

205 

238 

211 

213 

213 

200 

228 

104 

2(10 

203 

203 

202 

200 

200 

201 

204 

208 

313 

217 

221 

222 

220 

999 

184 

192 

195 

107 

107 

196 

197 

100 

203 

208 

215 

Ml 

226 

230 

22!) 

230 

174 

182 

187 

189 

190 

190 

192 

105 

200 

207 

216 

223 

230 

235 

237 

231 

163 

172 

177 

181 

182 

183 

186 

100 

196 

234 

214 

223 

231 

238 

241 

232 

153 

161 

167 

172 

173 

175 

178 

183 

100 

100 

210 

220 

230 

839 

243 

233 

142 

151 

157 

162 

164 

167 

170 

175 

183 

102 

204 

215 

227 

236 

213 

234 

131 

140 

147 

152 

155 

158 

161 

167 

174 

184 

196 

209 

221 

232 

240 

235 

120 

130 

137 

142 

145 

148 

152 

157 

165 

175 

187 

200 

213 

225 

231 

236 

110 

119 

127 

132 

136 

130 

142 

147 

155 

165 

177 

190 

203 

215 

225 

237 

99 

109 

117 

123- 

126 

120 

132 

137 

114 

153 

165 

178 

102 

234 

215 

238 

80 

09 

107 

113 

117 

110 

122 

127 

133 

1-12 

153 

166 

179 

192 

203 

230 

80 

89 

97 

103 

107 

110 

112 

lib 

122 

130 

140 

153 

166 

179 

101  . 

HMO 

71 

•   80 

88 

94 

98 

100 

102 

104 

110 

117 

127 

140 

153 

1  65 

177 

i 

The  perturbations  are  expressed  in  hundrudtlis  of  a  second  of  arc. 


TABL.E   XXII. 


/'<  rlurtiiiliuii.-:  iift/i*'  l.ninjititilf  lnj  the  Eurtli. 

lliiri/iuiiiil  Aiguiiiriit  =  I. 

•lit  milled  I"  i  i           I1,  riod  Of  U]  .-lit  XI  ,  -JIH  units. 

,i 

,i 

,i 

,i     ,i 

.1 

t 

ii 

.1 

,1 

.1 

d 

,1 

.1 

Arg.Xl 

120 

law 

i:t<i 

191 

132 

ICO 

1<>M 

170 

INI 

l«2 

200 

20* 

210 

UN 

232 

ISO 

211 

•j-ji 

936 

•Jll 

848 

948 

943 

833 

999 

807 

195 

183 

171 

167 

Hi) 

181 

193 

208 

•J-JI 

23d 

339 

849 

831) 

939 

899 

900 

l!>7 

1-5 

17.-. 

L67 

IG3 

1-.' 

IT:. 

190 

805 

918 

898 

933 

834 

'J'J!  1 

829 

910 

198 

186 

I7(i 

168 

163 

183 

IG6 

ITS 

I-- 

903 

816 

•J'J  1 

•,'•.'7 

22:. 

880 

•Jin 

109 

1-7 

71, 

168 

169 

l-l 

13d 

IM 

171 

188 

809 

213 

910 

817 

•Jll!) 

199 

188 

77 

168 

169 

186 

121 

137 

155 

179 

I-- 

801 

810 

•Jl  1 

913 

908 

111!) 

188 

7- 

168 

nil 

l-i, 

106 

131 

139 

107 

175 

100 

801 

809 

805 

198 

180 

7!l 

169 

n,i 

187 

n 

101 

195 

III 

169 

179 

199 

801 

804 

•:  a 

197 

189 

7!) 

169 

Mil 

188 

81 

96 

119 

131 

160 

168 

183 

194 

800 

•j  i  i 

11)6 

189 

1711 

169 

160 

160 

72 

>:, 

mi 

130 

140 

169 

17.-. 

187 

195 

197 

196 

189 

180 

170 

160 

180 

65 

77 

99 

111 

131 

ISO 

167 

181 

190 

104 

194 

i  m 

l-l 

171 

li,l 

1!H 

Gl) 

71 

1(13 

199 

149 

160 

17.-, 

I-:. 

191 

199 

188 

189 

I7'J 

162 

1'.i2 

57 

66 

79 

96 

115 

135 

153 

Ill:' 

181 

188 

190 

188 

183 

171 

n.l 

193 

G6 

63 

7:. 

mi 

10- 

198 

117 

!(.:< 

17G 

185 

18!) 

188 

l-l 

17G 

166 

1U4 

55 

60 

71 

85 

102 

121 

140 

157 

171 

181 

187 

188 

185 

179 

169 

I!).") 

Gfi 

60 

G7 

80 

96 

115 

133 

151 

166 

177 

I-:, 

188 

l-(i 

l-l 

171 

106 

66 

:.- 

64 

76 

90 

108 

137 

144 

160 

17)1 

I^'J 

186 

1-7 

l-l 

178 

1(17 

67 

67 

69 

72 

-:. 

101 

11!) 

137 

153 

167 

178 

185 

187 

186 

189 

108 

69 

57 

60 

68 

79 

95 

119 

139 

146 

nil 

173 

189 

187 

188 

185 

100 

Gl 

58 

58 

64 

74 

88 

104 

121 

139 

154 

168 

178 

185 

188 

188 

200 

lit 

58 

57 

60 

69 

81 

97 

113 

130 

146 

161 

17:! 

182 

187 

189 

Ml 

G7 

68 

66 

57 

(il 

7r, 

89 

105 

139 

138 

153 

166 

177 

184 

I-- 

909 

71 

61 

56 

.-,:, 

60 

69 

82 

'.17 

113 

139 

145 

159 

170 

I7!l 

1-:. 

903 

76 

G4 

57 

54 

67 

(il 

75 

89 

104 

130 

135 

150 

162 

172 

180 

904 

80 

67 

58 

54 

55 

61 

6!) 

82 

96 

111 

196 

140 

153 

164 

173 

205 

85 

71 

61 

66 

.'I 

58 

65 

75 

88 

101 

116 

129 

1  t-j 

154 

164 

106 

90 

76 

G4 

57 

54 

56 

61 

70 

81 

99 

105 

118 

131 

142 

159 

207 

95 

80 

68 

60 

56 

56 

51) 

66 

74 

-1 

96 

107 

II!) 

139 

110 

208 

Kid 

85 

72 

61 

57 

56 

:,7 

69 

69 

77 

87 

96 

107 

116 

136 

20!) 

105 

90 

77 

67 

60 

57 

56 

60 

65 

71 

78 

-ii 

!)5 

103 

112 

210 

10!) 

94 

81 

70 

62 

58 

56 

58 

61 

66 

71 

.77 

84 

91 

98 

211 

119 

97 

84 

73 

65 

60 

57 

57 

60 

62 

65 

(ill 

71 

7!) 

86 

Bit! 

114 

100 

87 

7G 

67 

61 

58 

57 

57 

59 

61 

-62 

66 

69 

74 

913 

115 

102 

•JO 

79 

69 

63 

59 

57 

56 

66 

57 

57 

59 

61 

65 

214 

116 

104 

91 

80 

71 

64 

60 

57 

56 

60 

55 

54 

55 

55 

57 

215 

117 

105 

93 

81 

72 

65 

60 

58 

56 

55 

54 

69 

52 

:.i 

61 

9H> 

118 

106 

94 

82 

73 

66 

61 

58 

57 

66 

.-,1 

51 

50 

4!) 

48 

217 

11!) 

107 

KS 

84 

75 

67 

62 

69 

58 

:.7 

.-,:, 

69 

50 

48 

46 

918 

121 

109 

97 

86 

76 

69 

64 

Gl 

69 

58 

57 

54 

52 

49 

46 

21!) 

194 

113 

100 

89 

79 

71 

66 

63 

61 

61 

59 

57 

55 

52 

48 

990 

129 

117 

104 

93 

83 

75 

6!) 

66 

64 

63 

69 

60 

58 

55 

61 

981 

1  35 

123 

111 

99 

88 

71) 

74 

70 

68 

68 

67 

(.1 

62 

60 

.-,:, 

993 

143 

131 

118 

106 

96 

86 

80 

7.-) 

73 

7'J 

79 

69 

67 

(il 

(in 

£33 

1  53 

141 

128 

116 

104 

94 

87 

82 

80 

7') 

77 

75 

73 

69 

Gl 

994 

164 

153 

140 

127 

115 

105 

97 

91 

87 

85 

84 

81 

7!) 

7:. 

6!) 

225 

177 

166 

153 

140 

128 

117 

108 

101 

97 

95 

!)2 

88 

85 

81 

7.-. 

226 

190 

180 

167 

K,4 

142 

130 

120 

113 

107 

103 

100 

96 

92 

87 

80 

9S7 

203 

193 

189 

16!) 

156 

III 

134 

125 

11!) 

114 

110 

105 

100 

94 

86 

228 

2  1  5 

21)7 

1!Ki 

Iri4 

171 

159 

148 

139 

131 

195 

120 

114 

108 

mi 

IK! 

999 

226 

21!) 

209 

198 

186 

173 

162 

152 

144 

137 

131 

194 

117 

108 

100 

930 

231 
232 
233 
234 

234 
241 

245 
24G 
244 

230 
238 
244 
246 
246 

221 
231 

338 

242 

244 

211 

222 
231 
2:56 
239 

19!) 
211 
221 
228 
232 

187 
900 

210 
218 
224 

176 

189 
200 
209 
216 

166 
178 

190 
200 
207 

157 

169 
181 
191 

200 

149 
161 
172 
183 
192 

142 
153 
165 

17.-, 
185 

134 
145 
156 

167 
177 

•127 
137 
148 
158 
169 

118 
ISti 
138 
149 
159 

109 
117 
187 

137 
148 

235 
236 
987 

sea 

939 

240 

240 
233 
224 
213 

201 

188 

243 
237 
229 
219 
207 
196 

242 
238 
231 
222 
211 
201 

239 
936 

230 
223 
214 
204 

233 
232 
938 
222 
214 
901 

227 
227 
224 
220 
213 
206 

220 
221 
220 
217 
212 
206 

913 

216 
217 
216 
919 

207 

206 
211 

•Jll 
•Jll 
•Jll 
209 

200 
206 
211 
212 
'JI3 

911 

1114 
201 
907 
911 
213 
213 

187 
196 
203 
208 
819 
814 

179 
189 
1*17 
•Jill 
210 
214 

170 
180 
190 
196 
908 
211 

ISO 

170 
180 

I'.M) 

1  - 

Add  147.64  to  Are.  XI.  when  224'>.7  is  subtracted  from  Arg.  I. 


40 


TABLE   XX1I1. 


Perturbations  of  the  Longitude  by  Mars. 

Horizontal  Argument  =  I. 

Constant  added  0'M3.         Period  of  Argument  1.,  224<1.7. 

Aif. 
XII. 

4 
0 

d 

i 

d 

16 

cl 

24 

d 

32 

d 

40 

i 

48 

d 

•158 

d 

61 

d 

72 

d 
80 

d 
88 

d 
96 

104 

d 

112 

0 

3 

4 

6 

9 

12 

15 

17 

20 

23 

24 

26 

26 

26 

26 

24 

1 

1 

2 

3 

5 

8 

11 

14 

17 

20 

22 

24 

26 

26 

26 

26 

2 

1 

1 

1 

3 

5 

8 

10 

14 

17 

19 

22 

24 

25 

26 

26 

3 

2 

1 

1 

1 

3 

5 

7 

10 

13 

16 

19 

21 

23 

24 

25 

4 

4 

2 

1 

1 

2 

3 

5 

8 

10 

13 

16 

18 

20 

22 

23 

5 

6 

4 

3 

2 

2 

2 

4 

6 

8 

11 

13 

16 

18 

20 

21 

6 

8 

6 

4 

3 

3 

2 

3 

5 

7 

9 

11 

14 

16 

18 

20 

7 

1! 

8 

6 

5 

4 

3 

4 

6 

6 

8 

10 

13 

15 

16 

18 

8 

12 

10 

8 

6 

5 

4 

4 

5 

6 

7 

9 

12 

14 

16 

18 

9 

14 

12 

10 

7 

6 

5 

5 

5 

5 

7 

9 

11 

13 

15 

17 

10 

15 

13 

11 

9 

7 

6 

5 

5 

5 

6 

8 

10 

12 

15 

17 

11 

17 

15 

13 

11 

8 

7 

5 

6 

5 

5 

7 

9 

II 

14 

16 

12 

18 

17 

15 

12 

10 

8 

6 

5 

5 

5 

6 

7 

9 

13 

15 

13 

20 

19 

17 

15 

12 

10 

8 

6 

6 

5 

5 

6 

8 

10 

13 

11 

21 

21 

19 

17 

15 

13 

10 

8 

6 

5 

5 

5 

6 

8 

10 

15 

22 

22 

21 

19 

17 

16 

13 

10 

8 

7 

6 

5 

6 

7 

9 

16 

21 

22 

22 

21 

19 

18 

15 

13 

11 

9 

7 

(i 

6 

6 

8 

17 

20 

21 

21 

21 

20 

19 

J8 

15 

13 

11 

9 

8 

7 

7 

7 

18 

17 

19 

20 

20 

20 

20 

19 

17 

15 

13 

11 

10 

9 

8 

8 

19 

15 

16 

18 

19 

19 

19 

19 

17 

16 

15 

13 

11 

10 

9 

9 

20 

13 

15 

15 

16 

17 

18 

18 

17 

16 

15 

14 

12 

11 

10 

10 

21 

12 

13 

14 

15 

15 

16 

16 

16 

15 

14 

13 

12 

11 

11 

10 

22 

12 

13 

13 

14 

14 

15 

15 

14 

14 

14 

13 

12 

11 

10 

10 

23 

13 

13 

14 

14 

14 

14 

14 

14 

13 

13 

12 

11 

10 

9 

9 

24 

15 

15 

15 

15 

15 

15 

14 

14 

13 

12 

12 

10 

9 

8 

8 

25 

10 

16 

16 

16 

16 

16 

16 

15 

14 

13 

12 

11 

9 

8 

7 

26 

16 

17 

17 

17 

17 

17 

17 

17 

16 

15 

13 

12 

10 

9 

7 

27 

16 

16 

17 

ifl 

18 

19 

19 

18 

18 

17 

15 

14 

12 

10 

8 

28 

14 

15 

16 

17 

18 

19 

19 

19 

19 

19 

18 

16 

14 

13 

11 

29 

12 

13 

14 

15 

16 

18 

19 

20 

20 

20 

19 

18 

17 

15 

13 

30 

10 

11 

11 

13 

14 

16 

17 

19 

20 

20 

20 

20 

19 

17 

15 

31 

0 

9 

9 

10 

12 

13 

15 

17 

18 

19 

20 

20 

19 

18 

17 

32 

!) 

9 

8 

9 

9 

11 

12 

14 

16 

17 

18 

19 

19 

19 

18 

33 

11 

9 

8 

8 

8 

9 

10 

12 

13 

15 

16 

17 

18 

18 

18 

34 

13 

11 

9 

8 

8 

8 

9 

10 

11 

12 

14 

15 

16 

16 

17 

35 

15 

13 

11 

10 

9 

8 

8 

9 

10 

11 

12 

13 

14 

15 

15 

36 

18 

16 

13 

11 

10 

9 

9 

9 

10 

10 

11 

12 

13 

14 

14 

37 

20 

18 

16 

14 

12 

10 

10 

10 

10 

10 

11 

12 

13 

14 

14 

38 

22 

20 

18 

15 

14 

12 

11 

11 

10 

11 

11 

12 

13 

14 

14 

39 

23 

21 

19 

17 

15 

13 

12 

11 

11 

11 

12 

13 

13 

14 

15 

40 

24 

23 

21 

18 

17 

15 

13 

12 

11 

11 

12 

13 

13 

14 

15 

41 

25 

24 

22 

20 

18 

16 

14 

13 

12 

11 

18 

12 

13 

14 

15 

42 

26 

25 

24 

22 

20 

18 

15 

14 

12 

12 

11 

12 

13 

14 

15 

43 

28 

27 

26 

24 

22 

23 

17 

15 

13 

12 

11 

12 

12 

13 

14 

44 

28 

28 

28 

26 

24 

22 

23 

17 

15 

13 

12 

11 

11 

12 

13 

45 

28 

29 

29 

28 

27 

25 

23 

20 

17 

15 

13 

12 

11 

11 

12 

46 

27 

28 

29 

29 

28 

27 

25 

23 

20 

18 

16 

14 

13 

12 

12 

47 

24 

26 

28 

29 

2!) 

28 

27 

25 

23 

20 

18 

16 

14 

13 

12 

48 

21 

24 

26 

27 

28 

28 

28 

26 

25 

23 

21 

19 

16 

15 

14 

49 

18 

20 

23 

25 

26 

27 

27 

27 

26 

24 

22 

20 

19 

17 

15 

50 

16 

17 

20 

22 

24 

25 

26 

26 

25 

25 

23 

22 

2!) 

18 

17 

51 

13 

15 

17 

19 

21 

23 

24 

24 

24 

24 

23 

22 

21 

19 

18 

52 

12 

14 

16 

17 

If) 

21 

22 

23 

21! 

23 

22 

21 

20 

19 

18 

53 

12 

13 

15 

17 

18 

20 

21 

21 

22 

22 

21 

21 

20 

19 

17 

54 

12 

14 

15 

17 

18 

19 

20 

21 

21 

21 

21 

20 

19 

18 

17 

55 

12 

14 

15 

17 

18 

23 

21 

21 

21 

21 

20 

20 

19 

18 

16 

56 

12 

14 

15 

17 

19 

2;) 

21 

22 

22 

22 

22 

21 

20 

18 

17 

57 

10 

12 

14 

17 

19 

20 

22 

2-3 

23 

24 

23 

22 

21 

20 

18 

58 

8 

10 

12 

\:> 

17 

20 

21 

23 

24 

25 

25 

24 

23 

22 

20 

59 

5 

7 

9 

12 

15 

17 

23 

22 

24 

25 

26 

26 

25 

24 

22 

6) 

3 

4 

6 

9 

12 

15 

17 

21 

23 

24 

26 

26 

26 

26 

24 

The  perturbation!  are  expressed  in  hundredth*  of  a  second  of  tin: 


TABLE    \\III. 


41 


Partarfaffow  »/'//«•  L«in>itu<li-  by  MII/-.I. 

ll"ii/unl;il  Ar«iiinrnr  =  I. 

<'i>ii<t:iin  aildnl  ()'  .!.">.                  IVnoil  ot'Argiiinriit  XII.,  GO  unite. 

Arg. 
XII 

lio 

a 
1«* 

.1 
136 

,1 
111 

.1 
1-52 

160 

I«N 

176 

ll 
INI 

-I 
192 

too 

SON 

.1 
216 

•J-JI 

•M 

0 

23 

81 

10 

17 

16 

13 

19 

11 

10 

10 

10 

II 

19 

14 

16 

1 

85 

2:1 

81 

1!) 

i; 

16 

14 

19 

11 

11 

11 

II 

ii 

19 

13 

*i 

K5 

M 

83 

89 

80 

Iti 

16 

16 

13 

18 

19 

II 

19 

19 

13 

:t 

85 

M 

83 

•21 

80 

18 

17 

15 

14 

13 

13 

13 

13 

1:1 

4 

M 

-,'l 

•21 

83 

89 

21 

19 

18 

17 

16 

16 

II 

14 

II 

11 

B 

22 

•,':i 

83 

88 

•J-' 

20 

I'.i 

IS 

17 

17 

16 

16 

16 

M 

K 

6 

21 

21 

81 

•.'i 

M 

80 

1!) 

18 

17 

16 

Hi 

H, 

Hi 

16 

16 

7 

80 

20 

•."i 

80 

19 

18 

17 

16 

Hi 

18 

16 

16 

16 

16 

8 

19 

•Ji 

80 

80 

19 

18 

17 

16 

16 

14 

II 

14 

14 

M 

K 

y 

19 

80 

80 

20 

1!) 

18 

17 

16 

15 

14 

13 

la 

I'J 

in 

14 

10 

19 

20 

21 

21 

21 

20 

18 

17 

16 

13 

12 

n 

II 

il 

II 

n 

18 

20 

21 

89 

•2-2 

81 

80 

18 

16 

II 

13 

n 

10 

!l 

10 

13 

17 

19 

21 

89 

23 

•j:t 

89 

•JI 

111 

Hi 

14 

12 

11    . 

!> 

:P 

13 

iii 

18 

•JI 

•J:t 

M 

M 

•.'I 

2:! 

21 

10 

17 

n 

N 

10 

9 

14 

13 

16 

19 

21 

23 

24 

•r. 

M 

2:1 

21 

N 

17 

14 

M 

111 

15 

11 

M 

17 

80 

22 

24 

86 

86 

25 

23 

22 

20 

17 

HS 

12 

ii; 

10 

19 

IS 

18 

20 

89 

M 

-.'.-, 

86 

86 

24 

22 

80 

17 

H 

17 

!) 

11 

13 

16 

Iti 

21 

23 

94 

86 

96 

96 

M 

22 

111 

17 

Iti 

!) 

in 

12 

14 

17 

W 

•.'1 

83 

86 

25 

85 

86 

98 

HI 

n 

1!) 

!) 

10 

11 

111 

re 

18 

20 

•,"-' 

M 

M 

•jr, 

25 

24 

23 

ll 

M 

10 

10 

n 

i:t 

K 

17 

1!) 

21 

B 

25 

86 

26 

m 

24 

sti 

1  I 

Id 

11 

N 

n 

16 

19 

81 

23 

M 

86 

26 

96 

•2r, 

•j; 

99 

!i 

10 

n 

12 

13 

15 

18 

20 

81 

•Ji 

2:> 

27 

27 

26 

9) 

83 

9 

!t 

9 

HI 

12 

14 

16 

1- 

22 

23 

25 

27 

27 

27 

•27 

24 

7 

7 

8 

9 

10 

N 

15 

17 

20 

22 

at 

26 

28 

28 

28 

15 

6 

6 

6 

6 

8 

10 

12 

14 

17 

20 

22 

25 

27 

28 

29 

% 

6 

.', 

5 

5 

5 

7 

9 

11 

14 

17 

20 

23 

2T> 

27 

88 

27 

7 

5 

5 

4 

4 

5 

6 

8 

11 

14 

16 

20 

•2-2 

25 

•27 

•J- 

8 

7 

5 

4 

4 

4 

4 

6 

8 

10 

18 

16 

l!l 

•2-2 

24 

29 

11 

0 

7 

5 

4 

4 

4 

5 

6 

8 

10 

13 

16 

I'.I 

21 

30 

13 

11 

9 

8 

6 

5 

4 

5 

5 

6 

8 

10 

13 

Hi 

18 

31 

i:. 

14 

12 

10 

8 

7 

6 

5 

r. 

6 

7 

9 

11 

13 

16 

n 

17 

15 

1:1 

12 

10 

9 

8 

7 

7 

7 

7 

8 

10 

12 

II 

33 

17 

16 

14 

13 

12 

10 

9 

8 

8 

8 

8 

9 

10 

12 

13 

34 

16 

15 

14 

13 

12 

11 

10 

9 

9 

9 

9 

10 

II 

12 

13 

35 

15 

15 

14 

13 

12 

11 

10 

9 

9 

9 

9 

10 

11 

12 

14 

86 

14 

14 

13 

12 

11 

10 

9 

9 

8 

8, 

9 

9 

10 

19 

14 

37 

14 

13 

IB 

12 

11 

9 

8 

8 

7 

7 

7 

8 

i 

11 

13 

38 

14 

14 

13 

12 

11 

9 

8 

7 

6 

5 

5 

6 

7 

!l 

II 

39 

15 

15 

14 

13 

11 

10 

8 

6 

5 

4 

4 

4 

5 

6 

8 

40 

16 

16 

15 

14 

13 

11 

9 

7 

5 

4 

3 

2 

3 

3 

."> 

II 

16 

17 

17 

16 

15 

13 

11 

9 

7 

5 

3 

2 

1 

2 

3 

42 

16 

17. 

17 

17 

17 

15 

14 

12 

9 

7 

5 

3 

2 

1 

1 

43 

16 

17 

18 

18 

18 

17 

16 

14 

12 

!l 

7 

5 

3 

1 

1 

44 

14 

16 

17 

18 

19 

18 

18 

17 

15 

12 

10 

7 

5 

It 

9 

45 

13 

14 

16 

17 

18 

19 

19 

18 

17 

15 

12 

10 

7 

5 

3 

46 

12 

19 

16 

16 

17 

n 

19 

18 

18 

16 

M 

12 

10 

8 

:. 

47 

13 

13 

14 

15 

16 

18 

18 

18 

18 

17 

Hi 

14 

12 

10 

8 

48 

13 

13 

14 

15 

16 

17 

18 

18 

18 

18 

17 

16 

14 

I-J 

10 

49 

15 

14 

14 

15 

16 

17 

17 

18 

18 

18 

18 

17 

16 

13 

II 

50 

16 

15 

15 

15 

16 

17 

17 

18 

19 

19 

19 

18 

17 

I.', 

13 

51 

17 

16 

16 

16 

16 

17 

18 

18 

19 

l!l 

111 

19 

1- 

17 

14 

52 

17 

16 

16 

16 

16 

17 

18 

19 

19 

20 

20 

20 

1!) 

18 

16 

5:1 

17 

16 

16 

IB 

16 

17 

17 

18 

20 

20 

21 

91 

21 

88 

Iri 

54 

16 

15 

15 

15 

15 

16 

17 

17 

19 

20 

21 

21 

89 

21 

20 

55 

If! 

14 

16 

13 

13 

14 

15 

1(i 

17 

19 

20 

21 

22 

88 

21 

56 

16 

14 

19 

12 

n 

l-> 

13 

14 

16 

17 

1- 

20 

21 

81 

•2-2 

57 

l(> 

14 

i:i 

12 

n 

11 

11 

n 

13 

15 

w 

1- 

l!l 

•ji 

21 

58 

18 

16 

II 

M 

n 

11 

10 

10 

11 

a 

14 

18 

17 

18 

19 

n 

20 

18 

16 

14 

13 

11 

10 

10 

10 

n 

11 

1:1 

14 

H, 

17 

6o 

23 

21 

19 

17 

15 

i:t 

12 

11 

10 

HI 

HI 

11 

u 

II 

IT. 

•M  19.6  to  Arg.  XII.  when  224d.7  is  subtracted  from  Arg.  I. 


TABLE  XXIV. 


Perturbations  of  the  Longitude  l»i  Jupiter. 

Horizontal  Argument  =  I. 

Constant  added  2".35.          1'eriod  of  Argument  I.  224ll.7. 

*  ,.— 

d 

a 

d 

d       d 

d 

d 

d 

d 

d 

d 

d 

d 

d 

d 

Aig. 
XIII. 

0 

§ 

16 

24 

32 

40 

48 

56 

64 

72 

§0 

8§ 

06 

1O4 

112 

0 

205 

209 

216 

226 

237 

248 

259 

268 

275 

278 

280 

279 

276 

271 

268 

1 

1  85 

184 

188 

194 

204 

214 

226 

236 

245 

253 

257 

25!) 

258 

256 

254 

a 

169 

164 

163 

166 

173 

182 

193 

204 

215 

221 

231 

237 

239 

240 

238 

3 

158 

147 

142 

111 

144 

151 

160 

171 

183 

194 

204 

212 

218 

221 

222 

4 

150 

136 

126 

121 

120 

123 

130 

140 

151 

163 

175 

186 

195 

201 

204 

5 

145 

12S 

115 

105 

100 

100 

104 

111 

121 

133 

146 

158 

1,0 

17!) 

185 

6 

143 

125 

108 

95 

86 

82 

82 

86 

04 

1  04 

117 

131 

144 

156 

164 

7 

143 

123 

1(15 

89 

77 

68 

64 

65 

70 

79 

90 

104 

118 

132 

143 

8 

143 

124 

105 

87 

72 

61 

53 

50 

52 

57 

67 

7!) 

93 

108 

121 

9 

143 

126 

108 

89 

72 

58 

47 

40 

38 

40 

47 

58 

71 

85 

100 

10 

142 

128 

111 

93 

75 

59 

46 

36 

30 

29 

32 

40 

51 

65 

79 

11 

140 

129 

115 

99 

81 

65 

4!) 

37 

28 

23 

23 

27 

36 

47 

61 

IS 

136 

.  129 

11!) 

105 

89 

73 

57 

42 

31 

23 

19 

20 

25 

34 

45 

13 

130 

128 

121 

111 

98 

83 

67 

52 

38 

28 

21 

18 

1!) 

25 

34 

14 

124 

125 

122 

116 

106 

94 

79 

61 

50 

37 

27 

21 

19 

21 

27 

15 

116 

120 

122 

120 

114 

105 

92 

73 

64 

50 

38 

29 

24 

22 

24 

16 

109 

115 

12!) 

122 

120 

115 

1C6 

94 

80 

66 

53 

42 

34 

28 

27 

17 

103 

111) 

117 

123 

125 

124 

119 

109 

98 

85 

71 

58 

48 

40 

35 

13 

96 

105 

114 

122 

129 

131 

130 

124 

116 

104 

91 

78 

65 

55 

47 

H 

92 

101 

111 

122 

131 

137 

140 

138 

133 

124 

112 

99 

85 

73 

63 

20 

ni 

99 

10) 

121 

132 

142 

149 

151 

149 

142 

133 

121 

108 

94 

82 

21 

92 

99 

108 

120 

133 

146 

166 

161 

163 

160 

153 

143 

131 

117 

104 

22 

95 

101 

10!) 

121 

135 

149 

161 

170 

176 

177 

173 

165 

154 

141 

128 

23 

100 

105 

112 

123 

136 

151 

166 

178 

187 

191 

190 

186 

177 

165 

152 

24 

108 

111 

118 

127 

139 

154 

170 

184 

196 

204 

206 

205 

199 

189 

177 

• 

117 

120 

125 

133 

144 

168 

174 

190 

203 

214 

220 

222 

219 

211 

201 

26 

128 

130 

131 

141 

ISO 

163 

178 

194 

210 

223 

232 

237 

237 

2i!2 

224 

27 

139 

142 

1  45 

151 

159 

170 

184 

199 

215 

230 

241 

24!) 

95S 

251 

245 

28 

151 

1  55 

158 

163 

169 

178 

190 

205 

220 

236 

219 

260 

266 

267 

264 

29 

164 

168 

171 

175 

180 

188 

198 

211 

226 

241 

255 

268 

277 

281 

281 

30 

177 

181 

165 

189 

194 

199 

207 

218 

231 

246 

261 

274 

285 

292 

906 

31 

190 

196 

200 

204 

208 

212 

218 

227 

238 

251 

265 

279 

991 

301 

307 

32 

204 

210 

215 

21!) 

222 

226 

230 

237 

245 

256 

269 

283 

296 

307 

316 

33 

21!) 

224 

229 

234 

237 

240 

243 

248 

254 

963 

273 

286 

299 

311 

322 

34 

235 

239 

241 

2-1!! 

252 

255 

257 

260 

264 

270 

278 

289 

301 

314 

326 

35 

251 

254 

259 

263 

267 

26!) 

271 

273 

275 

278 

284 

292 

303 

315 

327 

36 

268 

270 

274 

278 

281 

284 

286 

286 

287 

988 

291 

297 

305 

315 

327 

37 

287 

287 

289 

292 

296 

298 

300 

300 

299 

299 

999 

302 

307 

316 

396 

38 

306 

304 

305 

306 

309 

311 

313 

313 

312 

310 

308 

308 

311 

316 

325 

39 

326 

322 

321 

aai 

322 

324 

325 

325 

324 

321 

318 

316 

316 

318 

324 

40 

346 

341 

337 

325 

335 

336 

337 

337 

336 

333 

328 

324 

321 

321 

324 

41 

366 

359 

354 

350 

348 

347 

348 

348 

346 

343 

339 

333 

32!) 

325 

325 

42 

386 

378 

37.) 

B65 

361 

358 

B68 

357 

356 

353 

348 

343 

336 

331 

327 

43 

405 

3% 

387 

379 

373 

369 

867 

366 

364 

362 

357 

351 

'344 

337 

331 

44 

422 

413 

403 

394 

386 

380 

375 

373 

371 

369 

365 

359 

352 

344 

336 

45 

436 

428 

418 

408 

398 

390 

383 

379 

376 

374 

371 

366 

359 

351 

341 

m 

447 

440 

431 

420 

409 

399 

391 

384 

381 

373 

375 

371 

365 

357 

347 

47 

4.  14 

450 

441 

4:il 

419 

408 

398 

390 

381 

381 

378 

374 

369 

362 

353 

48 

'  457 

455 

44!) 

43!l 

428 

415 

404 

394 

367 

332 

378 

375 

371 

365 

357 

49 

455 

456 

452 

414 

433 

421 

409 

398 

388 

382 

378 

371 

371 

367 

860 

50 

448 

452 

451 

446 

436 

425 

412 

400 

38!) 

381 

376 

372 

369 

366 

861 

51 

436 

443 

445 

442 

435 

426 

413 

401 

889 

380 

373 

363 

365 

363 

359 

52 

419 

429 

434 

434 

430 

423 

412 

4(10 

388 

377 

36!) 

363 

360 

358 

355 

53 

897 

410 

413 

421 

421 

416 

407 

396 

384 

373 

364 

357 

353 

350 

349 

54 

372 

386 

397 

404 

406 

404 

398 

389 

378 

363 

358 

350 

345 

342 

341 

55 

344 

35!) 

372 

381 

386 

388 

385 

379 

370 

360 

351 

342 

336 

332 

331 

56 

315 

32!) 

343 

354 

362 

367 

368 

365 

358 

350 

341 

333 

326 

322 

320 

57 

385 

298 

312 

:'.2  1 

335 

342 

346 

346 

343 

337 

330 

333 

315 

310 

307 

68 

2:.6 

967 

279 

202 

304 

313 

380 

324 

324 

321 

316 

310 

304 

298 

905 

59 

2','!) 

2:',7 

217 

850 

271 

281 

991 

2!  17 

301 

301 

299 

296 

990 

2-5 

282 

ft 

205 

209 

216 

326 

237 

248 

25!) 

26s 

275 

278 

960 

279 

276 

271 

263 

The  perturbations  are  expressed  in  liundreilllis  of  a  seeond  of  arc. 


TABLE   XXIV. 


43 


Perturbations  <>/'  tin-  Longitude  In/  Jii/ii/cr. 

Horizontal  Arguinanl  =  1. 

Constant  added    I                             lVri.,.l  nCAr^mn.  -ul  Mil  .  (i  '  units. 

Arg. 
XIII 

120 

12N 

i:j« 

ail 

,i 

160 

ION 

176 

1*1 

.1 

»00 

20* 

,i 
216 

221 

2«2 

0 

965 

964 

966 

949 

189 

172 

157 

117 

1 

251 

250 

251 

959 

861 

946 

1-7 

168 

150 

136 

2 

936 

935 

935 

936 

937 

817 

1-5 

11,0 

146 

190 

3 

891 

....  , 

910 

919 

.j.j  , 

-Ml 

999 

991 

2I-* 

910 

198 

I-:; 

11,1 

146 

196 

4 

905 

206 

801 

199 

17:' 

163 

146 

195 

5 

188 

1-  i 

180 

188 

188 

188 

190 

191 

191 

i-  i 

l-l 

175 

161 

115 

196 

6 

171 

171 

171 

171 

173 

171 

175 

176 

I7li 

171 

168 

158 

1  II 

198 

7 

169 

157 

nit 

160 

160 

150 

168 

I.V.I 

n,i 

169 

169 

159 

153 

143 

190 

8 

139 

140 

146 

1  17 

117 

146 

1  15 

1  15 

i  I,, 

148 

1  i  • 

II!' 

147 

140 

130 

11 

113 

193 

134 

134 

139 

139 

139 

134 

I:  - 

138 

136 

ISO 

10 

83 

105 

115 

191 

193 

193 

I'-!'.' 

190 

190 

191 

193 

I-J7 

190 

130 

!'.'- 

II 

75 

100 

106 

1  12 

II  1 

113 

III 

IM 

110 

119 

115 

i-.'o 

193 

194 

12 

69 

73 

- 

96 

Ml 

104 

M", 

103 

109 

mi 

109 

M5 

no 

115 

11!) 

13 

46 

69 

79 

88 

01 

96 

98 

97 

94 

94 

97 

101 

M7 

114 

14 

36 

48 

60 

72 

81 

-- 

99 

91 

89 

89 

101 

109 

15 

31 

40 

51 

69 

73 

81 

86 

88 

88 

87 

85 

86 

89 

96 

104 

16 

80 

36 

45 

66 

66 

75 

39 

85 

86 

96 

-1 

84 

87 

92 

101) 

17 

34 

37 

43 

52 

61 

71 

78 

86 

86 

85 

85 

87 

!)() 

1- 

43 

42 

15 

51 

69 

68 

76 

82 

88 

88 

86 

89 

98 

1!) 

16 

89 

52 

:,:, 

60 

68 

75 

89 

-7 

91 

09 

93 

93 

06 

100 

20 

73 

66 

69 

62 

65 

70 

77 

84 

90 

95 

97 

98 

II!) 

101 

105 

21 

93 

77 

7:! 

7:! 

76 

81 

87 

94 

99 

103 

105 

107 

109 

119 

115 

103 

94 

88 

85 

88 

93 

106 

110 

113 

IHi 

118 

181 

98 

189 

196 

115 

106 

100 

98 

Ml 

UK; 

119 

M8 

122 

126 

12!) 

181 

84 

163 

150 

137 

127 

118 

113 

111 

112 

116 

101 

127 

132 

136 

140 

143 

25 

188 

175 

162 

150 

139 

132 

127 

126 

198 

132 

137 

142 

148 

152 

156 

M 

213 

900 

1-7 

171 

169 

153 

146 

!  13 

1  12 

1  II 

i  ri 

164 

169 

16.5 

16!) 

9? 

986 

996 

819 

199 

1-7 

176 

167 

162 

169 

l.v.i 

IfiSI 

166 

179 

178 

1*3 

98 

968 

248 

237 

•-"J  1 

212 

900 

190 

183 

178 

17(1 

177 

1-1 

186 

191 

P.  17 

277 

270 

260 

949 

987 

095 

214 

206 

100 

196 

104 

196 

200 

905 

211 

3D 

986 

290 

282 

273 

262 

250 

240 

230 

222 

216 

•.'i:i 

213 

216 

220 

226 

31 

309 

807 

302 

996 

286 

275 

965 

255 

946 

939 

934 

232 

2:i:i 

236 

240 

32 

321 

899 

390 

815 

308 

899 

989 

96  > 

270 

969 

252 

861 

253 

256 

330 

834 

335 

333 

898 

321 

313 

304 

996 

286 

870 

•J7I 

271 

970 

872 

84 

336 

349 

347 

348 

346 

341 

335 

398 

31!) 

311 

303 

991 

289 

86 

339 

848 

355 

359 

361 

359 

866 

350 

849 

834 

887 

819 

313 

308 

886 

36 

340 

351 

360 

368 

379 

371 

373 

360 

864 

857 

350 

849 

034 

32!) 

:!•.'  l 

37 

338 

351 

362 

372 

380 

886 

887 

386 

883 

37fl 

372 

864 

866 

349 

343 

336 

849 

361 

374 

384 

399 

398 

400 

1  •« 

807 

399 

886 

370 

369 

::;i 

333 

315 

358 

372 

385 

396 

410 

413 

413 

110 

405 

898 

889 

:;-! 

40 

330 

340 

353 

368 

889 

396 

407 

416 

422 

425 

486 

422 

416 

408 

399 

41 

328 

336 

361 

376 

899 

406 

4IH 

1-7 

434 

436 

435 

431 

494 

416 

40 

397 

839 

340 

363 

368 

384 

101 

416 

498 

437 

443 

445 

III 

130 

43 

898 

389 

3:!4 

345 

358 

375 

3!>2 

409 

494 

437 

446 

451 

469 

449 

443 

44 

380 

32-i 

329 

337 

348 

363 

3SO 

899 

416 

431 

443 

452 

466 

455 

151 

43 

:!:!:! 

888 

326 

330 

338 

351 

367 

I    1 

421 

436 

II- 

466 

46 

330 

393 

394 

329 

352 

870 

388 

407 

421 

439 

449 

455 

47 

343 

333 

885 

321 

897 

838 

353 

371 

390 

408 

us 

447 

|5| 

48 

347 

887 

887 

!il!) 

315 

317 

324 

336 

359 

370 

407 

422 

184 

441 

49 

351 

341 

329 

319 

312 

309 

312 

320 

889 

848 

367 

385 

1    .' 

416 

496 

50 

353 

344 

332 

:!•-'! 

311 

304 

302 

305 

314 

397 

843 

36  > 

37- 

804 

406 

51 
52 

863 

346 

345 

886 
836 

323 

32  1 

311 
312 

801 
909 

2!  15 
2!H) 

293 
984 

306 

319 

835 

300 

361 

:•••>  1 

868 
840 

889 

355 

53 

'illi 

342 

335 

3-.'5 

313 

987 

277 

271 

275 

:ilo 

325 

54 

339 

337 

332 

884 

313 

889 

285 

273 

989 

100 

269 

980 

908 

55 

57 
58 
60 

60 

330 
819 
306 
903 

'-'Ii5 

329 
819 
307 
294 
879 
964 

326 
318 

307 
295 
280 
265 

320 
311 
305 
996 
381 
266 

311 

-'-I 
967 

297 
903 
987 

978 

266 

284 

2-1 
277 
•J7I 
262 

270 
368 
266 
264 

254 

257 

948 

•.•  1  -. 
949 

247 
999 

998 

241 
229 
2.'  ' 
914 
2ID 

240 
910 

193 

l-  i 

944 

999 
804 

i-  i 
I7'J 
179 

252 
895 

I6tl 

157 

96)1 

233 
1-.' 

ii,-.: 

147 

Add  3.11  to  Arg.  XIII.  when  224<l.7  is  subtract.;,!  Inmi  Arg.  1. 

1    1      IT 

44 


TABLE  XXV. 


Perturbations  of  the  Longitude  by  Satiini. 

Horizontal  Argument  =  I. 

Constant  added  0".40.                        Period  of  Argument  I.,  224i'.7. 

Ar«. 
XIV. 

a 
o 

d 

9 

a 

16 

d 
24 

d 
32 

d 
40 

d 

4§ 

(1 
56 

d 
64 

d 
72 

d 

80 

d 
S§ 

d 
96 

d 
104 

d 
112 

0 

39 

43 

47 

54 

GO 

66 

72 

77 

80 

81 

81 

80 

78 

75 

72 

1 

37 

39 

43 

48 

54 

01 

67 

72 

77 

79 

80 

80 

79 

76 

74 

a 

36 

36 

39 

43 

48 

54 

61 

67 

72 

76 

78 

79 

78 

77 

74 

3 

36 

Oft 

35 

fj/t 

35 

OO 

38 

0,1 

42 
da 

47 
Jn 

54 

AC 

60 

66 

Rn 

71 
fid 

75 
an 

77 

77 

76 

74 

5 

OO 

37 

O4 

34 

OO 

31 

O** 

30 

ou 
31 

<*u 
34 

4o 
39 

52 
44 

ov 
51 

0*1 
57 

Ut/ 

63 

67 

70 

71 

71 

c 

38 

34 

31 

28 

28 

2!) 

32 

37 

42 

49 

55 

60 

C5 

67 

68 

7 

38 

34 

31 

27 

25 

25 

27 

30 

34 

40 

46 

52 

58 

62 

64 

8 

38 

34 

31 

27 

24 

22 

22 

24 

27 

33 

38 

44 

50 

55 

59 

9 

37 

34 

31 

27 

23 

21 

19 

19 

21 

25 

30 

35 

42 

47 

52 

10 

35 

33 

30 

26 

23 

19 

17 

16 

1C 

18 

22 

27 

33 

39 

45 

11 

33 

31 

29 

26 

22 

19 

16 

14 

13 

14 

16 

20 

25 

31 

37 

12 

30 

29 

27 

25 

22 

19 

15 

12 

11 

10 

11 

14 

18 

24 

29 

13 

27 

do 

25 

23 

21 

18 

15 

12 

9 

8 

8 

9 

12 

17 

22 

14 

25 

24           23 

22 

20 

18 

15 

12 

9 

7 

6 

G 

8 

11 

16 

15 

2:1 

22           21 

20 

19 

17 

15 

12 

9 

7 

5 

4 

5 

7 

11 

1C 

a:i 

21 

20 

19 

18 

16 

15 

13 

10 

8 

5 

4 

3 

4 

7 

17 

24 

21 

19 

18 

17 

1G 

15 

13 

11 

8 

6 

4 

3 

3 

4 

18 

26 

23 

20 

19 

17 

16 

15 

13 

12 

10 

7 

5 

4 

3 

3 

19 

29 

26 

23 

20 

19 

17 

16 

15 

13 

11 

9 

7 

5 

4 

3 

20 

33 

30 

26 

23 

21 

19 

18 

16 

15 

13 

11 

9 

7 

5 

4 

21 

38 

34 

31 

27 

25 

22 

20 

19 

17 

16 

14 

12 

10 

8 

6 

22 

42 

39 

36 

32 

29 

26 

24 

22 

20 

19 

17 

15 

13 

11 

9 

23 

46 

44 

42 

38 

35 

32 

29 

27 

24 

22 

21 

19 

17 

15 

13 

24 

50 

50 

47 

44 

41 

38 

34 

32 

29 

27 

25 

23 

21 

19 

17 

25 

54 

54 

53 

50 

47 

44 

41 

38 

35 

32 

30 

28 

26 

24 

22 

26 

56 

58 

57 

56 

54 

51 

47 

44 

41 

38 

36 

34 

31 

29 

27 

27 

.  58 

60 

61 

61 

59 

57 

54 

51 

48 

44 

42 

39 

37 

35 

32 

28 

58 

62 

64 

65 

65 

63 

60 

57 

54 

51 

48 

45 

43 

41 

36 

29 

58 

63 

66 

68 

69 

68 

66 

63 

60 

57 

54 

51 

49 

47 

44 

30 

57 

62 

67 

70 

72 

72 

71 

69 

66 

63 

60 

57 

55 

52 

50 

31 

54 

61 

66 

70 

73 

75 

75 

74 

71 

69 

66 

63    • 

60 

57 

55 

32 

52 

58 

64 

69 

74 

76 

77 

77 

76 

73 

71 

68 

65 

62 

60 

33 

48 

55 

61 

67 

72 

76 

79 

79 

79 

77 

75 

72 

69 

67 

64 

34 

45 

51 

57 

64 

69 

74 

78 

80 

81 

80 

78 

76 

73 

70 

68 

35 

42 

47 

52 

59 

65 

71 

76 

79 

81 

81 

80 

78 

76 

73 

70 

36 

39 

43 

47 

54 

60 

66 

72 

77 

80 

81 

81 

80 

78 

75 

72 

The  perturbations  are  expressed  in  hundredths  of  a  second  of  arc. 

TAIILI-:  xxv. 


/'•  rtitrliiilitiH.-i  nfl/if  /,.>»'/<>("/<•  />;/  Kilurn. 

linn,                           audit  =  I 

CiHisluiit  iiddvd  II".  lil.                    IViind  i.C  .  \rgmi  i.-nl  XIV.,  M  units. 

\  r** 

.1 

d 

d 

.1 

d 

d 

d 

.1 

d 

,! 

d 

d 

d 

d 

XIV. 

i*o 

I3M 

186 

III 

154 

100 

ION 

170 

ISI 

200 

SON 

310 

9JM 

3»3 

0 

70 

G8 

60 

83 

61 

68 

69 

18 

4r. 

41 

37 

87 

40 

1 

71 

00 

67 

88 

63 

0] 

5! 

47 

44 

40 

88 

80 

37 

g 

72 

60 

87 

03 

61 

57 

64 

46 

43 

80 

86 

3 

79 

(i'.p 

87 

64 

83 

61 

60 

67 

55 

69 

1- 

44 

40 

8fl 

34 

4 

71 

00 

in; 

64 

09 

60 

68 

49 

45 

41 

37 

34 

5 

70 

88 

68 

69 

60 

68 

56 

06 

83 

69 

40 

40 

19 

34 

6 

68 

86 

in 

01 

56 

54 

61 

50 

48 

M 

42 

SB 

36 

7 

88 

64 

69 

60 

67 

:.| 

59 

60 

48 

47 

41) 

44 

49 

38 

86 

8 

00 

61 

GO 

68 

59 

49 

47 

40 

44 

43 

1-' 

40 

34 

9 

56 

57 

57 

66 

63 

50 

47 

46 

43 

41 

40 

30 

86 

34 

10 

49 

69 

53 

53 

51 

49 

M 

43 

40 

88 

37 

36        :i.i 

34 

39 

11 

49 

46 

4'.) 

60 

49 

47 

45 

49 

38 

36 

34 

33          31 

31 

29 

19 

I!.-, 

40 

41 

46 

47 

46 

44 

41 

38 

86 

32 

30 

28 

27 

13 

18 

83 

38 

42 

43 

44 

43 

40 

37 

34 

31 

29 

27 

26 

94 

14 

91 

27 

32 

37 

40 

41 

41 

40 

37 

34 

31 

28 

96 

•Jl 

93 

16 

18 

21 

27 

32 

36 

39 

40 

39 

38 

35 

32 

28 

96 

23 

21 

16 

11 

16 

21 

27 

32 

86 

33 

80 

36 

33 

30 

27 

24 

M 

17 

7 

11 

10 

99 

28 

89 

36 

38 

89 

38 

86 

89 

29 

96 

93 

18 

5 

8 

13 

1- 

93 

29 

83 

37 

38 

39 

37 

35 

39 

29 

to 

4 

6 

10 

15 

20 

25 

31 

35 

33 

40 

40 

38 

36 

39 

20 

4 

6 

8 

12 

17 

23 

28 

33 

33 

40 

41 

41 

40 

37 

33 

91 

6 

6 

8 

11 

15 

20 

26 

3C 

37 

40 

43 

44 

43 

41 

38 

99 

8 

8 

9 

11 

14 

19 

24 

30 

86 

40 

44 

46 

47 

48 

43 

93 

11 

10 

10 

12 

14 

18 

23 

23 

84 

39 

44 

47 

49 

4!) 

43 

•Jl 

16 

13 

13 

13 

15 

18 

99 

27 

33 

39 

44 

48 

51 

53 

63 

96 

19 

17 

16 

16 

16 

18 

22 

2G 

32 

38 

43 

49 

53 

.-,:, 

50 

90 

24 

22 

20 

19 

19 

20 

22 

26 

31 

36 

43 

48 

53 

57 

5'J 

27 

30 

27 

25 

23 

99 

22 

23 

26 

30 

35 

41 

47 

53 

61 

28 

35 

33 

30 

28 

26 

25 

25 

27 

30 

34 

40 

46 

52 

58 

02 

29 

41 

39 

3G 

33 

30 

29 

28 

28 

30 

34 

38 

44 

50 

57 

69 

30 

47 

44 

41 

38 

35 

33 

31 

30 

31 

33 

37 

42 

48 

68 

60 

31 

53 

60 

47 

44 

41 

38 

35 

33 

33 

34 

36 

40 

46 

69 

32 

57 

55 

52 

49 

46 

42 

39 

36 

86 

34 

86 

39 

43 

49 

66 

:i:i 

63 

GO 

57 

54 

51 

47 

44 

40 

38 

36 

36 

37 

41 

45 

51 

34 

65 

63 

61 

58 

55 

52 

48 

45 

41 

39 

37 

37 

39 

42 

47 

35 

68 

66 

64 

61 

59' 

56 

53 

49 

48 

41 

39 

37 

38 

39 

43 

36 

8j 

70 

63 

66 

63 

61 

59 

" 

52 

48 

45 

41 

38 

37 

37 

40 

Add  0.8  to  Arg.  XIV.  when  224-'.7  ia  subtracted  from  Arg.  I. 

TABLE  XXVI. 


Lntrarillim  of  the  Elliptic  Radius  Vector  for  BBS  =  0. 
Constant  subtracted  0.0000257.        Period  of  Argument  I.  'J'JI'1.7008. 

Arg.  I. 

a 
O.O 

a 
0.1 

a 
O.2 

d 
0.3 

a 
0.4 

a 
O.5 

ii 
O.G 

a 
0.7 

d 
0.8 

a 
O.9 

UilT. 
for  0-1.1. 

a 

0 

9.8563298 

63298 

63298 

63299 

63300 

63301 

63302 

63304 

63305 

63307 

+  1 

1 

63310 

63312 

63315 

63318 

63321 

63324 

63328 

63332 

63336 

63341 

4 

2 

63345 

63350 

^3355 

63360 

63366 

63372 

63378 

63384 

63391 

63397 

6 

3 

63404 

63412 

63419 

63427 

63435 

63443 

63451 

63460 

63469 

63478 

8 

4 

63487 

63497 

63507 

63517 

63527 

63538 

635  18 

63559 

63571 

63582 

11 

5 

63594 

63606 

63618 

63630 

63643 

63656 

C3669 

63682 

63696 

63710 

13 

6 

63724 

63738 

63752 

63767 

63782 

63797 

63813 

63828 

63844 

63860 

15 

7 

63877 

63893 

63910 

63927 

63945 

63962 

63980 

63998 

64016 

64035 

18 

8 

64053 

64072 

64092 

64111 

64131 

64150 

64171 

64191 

64211 

64232 

20 

9 

64253 

64274 

64296 

64317 

64339 

64362 

64384 

64407 

64429 

64452 

22 

10 

64476 

64499 

64523 

64547 

64571 

64595 

64620 

64645 

64670 

64695 

25 

11 

64721 

64747 

64773 

64799 

64825 

64852 

64879 

64906 

64933 

64961 

27 

12 

64989 

65017 

65045 

65073 

65102 

65131 

65160 

65189 

65219 

65249 

29 

13 

65279 

65309 

65340 

65370 

65401 

65432 

65464 

65495 

65527 

65559 

31 

14 

65591 

65624 

65656 

65689 

65722 

65756 

65789 

65823 

65857 

65891 

33 

15 

65925 

65960 

65995 

66030 

66065 

66100 

66136 

66172 

66208 

66244 

36 

16 

66281 

66318 

66354 

66392 

66429 

66467 

66504 

66542 

66581 

66619 

38 

17 

66658 

66697 

66736 

66775 

66814 

66854 

66894 

66934 

66974 

67015 

40 

18 

67055 

67096 

67137 

67179 

67220 

67262 

67304 

67346 

67388 

67431 

42 

19 

67474 

67517 

67560 

67603 

67647 

67691 

67734 

67779 

67823 

67868 

44 

20 

67912 

67957 

68002 

68048 

68093 

68139 

68185 

68231 

68278 

68324 

46 

21 

68371 

68418 

68465 

68512 

68560 

68609 

68656 

68704 

68752 

68800 

48 

22 

68849 

68898 

68947 

68996 

69046 

69095 

69145 

69195 

69245 

69296 

50 

23 

69346 

69397 

69448 

69499 

69550 

69602 

69654 

69706 

69758 

69810 

52 

24 

69862 

69915 

69968 

70021 

70074 

70127 

70181 

70234 

70288 

70342 

53 

25 

70396 

70451 

70505 

70560 

70615 

70670 

70726 

70781 

70837 

70893 

55 

.  26 

70949 

71005 

71061 

71118 

71174 

71231 

71288 

71345 

71403 

71460 

57 

27 

71518 

71576 

71031 

71692 

71751 

71809 

71868 

71927 

71986 

72045 

59 

28 

72105 

72164 

72224 

72284 

72344 

72404 

72464 

72525 

72586 

72646 

60 

29 

72707 

72769 

72830 

72891 

72953 

73015 

.73077 

73139 

73201 

73264 

62 

30 

73326 

73389 

73452 

73515 

73578 

73642 

73705 

73769 

73833 

73897 

63 

31 

73961 

74025 

74089 

74154 

74219 

74284 

74319 

74414 

74479 

74544 

65 

1 

32 

74610 

74676 

74742 

74808 

74874 

74940 

75007 

75073 

75140 

75207 

66 

33 

75274 

75341 

75408 

75476 

75543 

75611 

75679 

75747 

75815 

75883 

88 

34 

75951 

76020 

76089 

76157 

76226 

76295 

76364 

76434 

76503 

76573 

69 

35 

76642 

76712 

76782 

76852 

76922 

76993 

77063 

77134 

77204 

77275 

70 

36 

77346 

77417 

77488 

77560 

77631 

77703 

77774 

77846 

77918 

77990 

72 

37 

78062 

78134 

78207 

78279 

78352 

78425 

78497 

78570 

78643 

78716 

7?i 

38 

78790 

78863 

78937 

79010 

79084 

79158 

79232 

79306 

79380 

79454 

74 

39 

79528 

79603 

79677 

79752 

79827 

79902 

79977 

80052 

80127 

80202 

75 

40 

80277 

80352 

80428 

80504 

80580 

80656 

80732 

80808 

80884 

80960 

76 

41 

81036 

81113 

81189 

81266 

81343 

81419 

81496 

81573 

81650 

81727 

77 

42 

81805 

81882 

81959 

82037 

82114 

82192 

82270 

82348 

82425 

82503 

78 

43 

82582 

82660 

82738 

82816 

82895 

82973 

83052 

83130 

83209 

83288 

78 

44 

83366 

83445 

83524 

83603 

83682 

83762 

83841 

83920 

84000 

84079 

79 

45 

84159 

84238 

84318 

84398 

84477 

84557 

84637 

84717 

84797 

84877 

80 

46 

84958 

85038 

85118 

85199 

85279 

85359 

85410 

85521 

85601 

85682 

81 

47 

9.8585763 

85844 

85924 

86005 

86086 

86167 

86249 

86330 

86411 

86492 

+  81 

TABLE  XXVI. 


47 


i-ithiH  of  1  In-  Klliptir  ]{u,liu*  V,  <•;,,,-  !.,,-  tjj  =  0. 
C.,ii!.t:iiit  ,.|i!itr:;rtril  (I.IIIMI 

Ar-.  I. 

.1 
0.0 

,1 
O.I 

.1 

cl 

.1 
0.1 

0..5 

.1 

.1 

o.r 

.1 
O.8 

j 
O.3 

for  ii 

.1 

' 

is 

9.8586573 

86655 

86736 

Mis  17 

86899 

86980 

870(12 

v,  1  1  1 

49 

>   N7171 

87552 

87716 

s77!is 

87880 

87962 

88!)  I] 

88126 

82 

50 
51 

88208 
89031 

S8290 
89111 

SS373 
89196 

89279 

89362 

88613 

8!)  1  1  1 

89527 

89609 

88861 

89692 

88!)  Ill 

81(775 

82 
83 

52 

89857 

s!)9  10 

90023 

90106 

90189 

90354 

ill)  137 

90520 

90608 

S3 

53 

90686 

90769 

908.V.' 

90934 

91017 

91100 

91183 

!H  266 

91349 

91432 

83 

51 

91516 

91599 

ill  68-_> 

91765 

91848 

91931 

9201  1 

92097 

92263 

55 

92316 

92  129 

92513 

92596 

92679 

92762 

92845 

!  12928 

98011 

930!)  1 

83 

56 

93177 

93260 

93311 

93  127 

93510 

93593 

98676 

9375!) 

938  12 

93925 

57 

94008 

91091 

94174 

1)1257 

91310 

!)  1  123 

91506   915V!) 

94672 

91755 

83 

58 

94838 

91921 

95001 

!  15086 

95169 

95252 

95335 

95118 

95500 

95583 

59 

95666 

957  1!) 

!  1583  1 

95911 

95996 

96079 

96162 

962  1  1 

96327 

96109 

83 

60 

96493 

9657  1 

96656 

• 

96821 

96903 

96986 

97068 

97150 

97232 

82 

61 

97311 

97396 

97478 

97560 

976  12 

9772  1 

97806 

!)7sss 

97970 

98052 

62 

98134 

98215 

98297 

98  160 

98542 

98623 

98705 

98786 

!IS8li7 

82 

63 

98949 

99030 

99111 

9!)  If  12 

99273 

99351 

99  135 

!)!).->  16 

99597 

99678 

81 

61 

9.6599759 

99839 

99920 

tooooi 

00081 

00162 

00212 

00323 

00103 

00183 

80 

65 

9.86005(13 

006  13 

00721 

(HIS01 

00684 

00963 

01013 

01123 

01203 

01282 

80 

66 

01362 

01112 

01  521 

01600 

01680 

0175!) 

01838 

011)17 

0191)6 

02075 

71) 

67 

02151 

02233 

02311 

023!IO 

02469 

02517 

02626 

02701 

02782 

02860 

78 

68 

02938 

03016 

030!)  1 

03172 

03250 

03328 

03105 

03483 

03560 

03638 

7s 

69 

03715 

03792 

03*69 

03!)  16 

01023 

01100 

01177 

0  125  1 

01330 

01107 

77 

70 

04483 

01560 

01636 

01712 

01788 

Ols6  I 

04940 

05016 

050!)  1 

05167 

7(1 

71 

052  12 

05:;  is 

05393 

05168 

05513 

05(518 

05693 

95768 

05843 

05917 

75 

72 

05992 

06066 

06110 

06215 

06289 

06363 

06136 

06510 

0658  1 

06657 

71 

73 

06731 

06801 

06877 

06950 

07023 

07096 

07169 

072  12 

07311 

07387 

73 

74 

0715!) 

07531 

07(i()3 

07675 

07717 

0781!) 

07891 

07962 

08031 

08105 

75 

08176 

082  17 

08318 

08389 

08460 

O.s530 

08601 

08671 

08711 

08811 

71 

76 

08881 

08951 

09021 

09090 

09160 

09229 

09298 

09367 

09136 

09505 

69 

77 

0957  1 

096  12 

09711 

09779 

098  17 

09915 

09983 

10051 

Kills 

10186 

68 

78 

10253 

10321 

10388 

10155 

10522 

10588 

10655 

1(1721 

10788 

10854 

67 

79 

10920 

10986 

11051 

11117 

11182 

1  12  is 

11818 

1  137s 

11113 

11507 

65 

80 

11572 

11636 

11701 

1  17(15 

11829 

11893 

11956 

12020 

12116 

64 

81 

12210 

12273 

12335 

12398 

12161 

12523 

12585 

12617 

1270!! 

12771 

62 

82 

12832 

12894 

12955 

13016 

13077 

13138 

13199 

13259 

13319 

13380 

61 

83 

13110 

13500 

13619 

13678 

13797 

13856 

13!ll  1 

13973 

5!) 

81 

1  1031 

11090 

1  11  is 

11206 

1  1263 

14321 

14878 

11136 

14499 

1  1550 

85 

14606 

1  1663 

1  1720 

1  1776 

1  1832 

1  ISSN 

14943 

1  1!)!)!) 

15051 

15110 

56 

86 

15165 

15220 

15275 

15329 

15384 

15438 

15499 

15546 

1551111 

15653 

54 

87 

15706 

1575!) 

15812 

15865 

15918 

15970 

16023 

16075 

16127 

16178 

52 

88 

16286 

16281 

16333 

16384 

16131 

Kits;, 

16536 

16586 

16636 

16686 

51 

89 

16736 

16785 

16835 

16933 

16982 

17031 

17079 

17127 

17175 

1!) 

90 

17223 

17271 

17319 

17366 

17113 

17160 

17.  --07 

17553 

17600 

17646 

17 

91 

17692 

17738 

17783 

17829 

17874 

17919 

17964 

18009 

18053 

180!  IS 

45 

K 

18142  |  18186 

18229 

18273 

18316 

I.s35!l 

Is  |(I2 

is  115 

18488 

18530 

43 

93 

18572   18614 

18656 

1S697 

18739 

18780 

18862 

Is!  102 

181113 

11 

18983   19023 

19063 

19102 

19112 

19181 

19250 

19258 

19297 

19335 

39 

95 

9.8619373   19411 

19449 

19487 

19521 

19561 

1115!  is 

19635 

19671 

19708  +37 

1 

TABL.E  XXVI. 


Logarithm  of  'tin-  Elliptic  E/i'/ina  Vector  for  IS1  =  0. 
Constant  subtracted  0.000(;:2.")7.        Period  of  Argument  I.  a24<>.7008. 

ArB.  I. 

,1 
O.O 

a 
0.1 

<i 
O.2 

a 
O.3 

a 
O.I 

a 

0.9 

<i 
0.6 

a 

o.y 

cl 

0.8 

a 
O.9 

Diff. 
fbrOM. 

d 

| 

96 

9.8619744 

19780 

19815 

19S51 

19886 

19921 

19956   19991 

20025 

20060 

+  35 

97 

20094 

20127 

20161 

20191 

20228 

20261 

20294 

20326 

20359 

20391 

33 

98 

20  123 

20454 

20186 

20517 

20548 

20579 

20610 

20641 

20671 

20701 

31 

99 

20731 

20760 

20790 

20819 

20848 

20877 

20905 

20934 

20962 

20990 

29 

100 

21017 

21045 

21072 

21099 

21126 

21153 

21179 

21205 

21231 

21257 

27 

101 

2128S 

21308 

21333 

21358 

21382 

21407 

21431 

21455 

21479 

21502 

24 

102 

21520 

21519 

21572 

21595 

21617 

21639 

21662 

21683 

21705 

21726 

22 

103 

21748 

21769 

21789 

21810 

21830 

21850 

21870 

21890 

21909 

21928 

20 

104 

21947 

21966 

21984 

22003 

22021 

22039 

22056 

22074 

22091 

22108 

18 

105 

22121 

22141 

22157 

22173 

22189 

22205 

22220 

22235 

22250 

222  G5 

16 

106 

22280 

2229-1 

22308 

22322 

22335 

22349 

22362 

22375 

22388 

22100 

13 

107 

22412 

•2-2  12  i 

22436 

22  1  18 

22459 

22470 

22481 

22492 

22502 

22512 

11 

108 

22522 

22532 

22542 

22551 

22560 

22569 

22577 

22586 

22594 

22602 

9 

109 

22610 

22617 

22625 

22632 

22639 

22645 

22651 

22658 

22663 

22669 

6 

110 

22675 

22680 

22685 

22690 

22694 

22699 

22703 

22707 

22710 

22714 

4 

111 

22717 

22720 

22723 

22725 

22727 

22729 

22731 

22733 

22734 

22735 

+2 

112 

22736 

22737 

22737 

22737 

22737 

22737 

22737 

22736 

22735 

22734 

0 

113 

22733 

22731 

22729 

22727 

22725 

22722 

22720 

22717 

22714 

22710 

—  3 

114 

22706 

22703 

22698 

22694 

22690 

22685 

22680 

22675 

22669 

22663 

5 

115 

22657 

22651 

22645 

22638 

22632 

22624 

22617 

22610 

22602 

22594 

7 

116 

22586 

22577 

22569 

22560 

22551 

22542 

22532 

22522 

22512 

22502 

9 

117 

22492- 

22481 

22470 

22.159 

22448 

22436 

22424 

22412 

22100 

22387 

12 

118 

22375 

22362 

22349 

22335 

22322 

22308 

2229  1 

22279 

22265 

22250 

14 

119 

22235 

22220 

22205 

22189 

22173 

22157 

22141 

22124 

22108 

22091 

16 

120 

22074 

22056 

22039 

22021 

22003 

21984 

21966 

21947 

21928 

21909 

18 

121 

21890 

21870 

21850 

21830 

21810 

21789 

21769 

21748 

21726 

21705 

21 

122 

21683  21662 

21639 

21617 

21595 

21572 

21549 

21526 

21503 

21479 

23 

123 

21455 

21431 

21107 

21383 

21358 

21333 

21308 

21283 

21257 

21231 

25 

124 

21205 

21179 

21153 

21126 

21099 

21072 

21045 

21017 

20990 

20962 

27 

125 

20934 

20905 

20877 

20848 

20819 

20790 

20760 

20731 

20701 

20671 

29 

126 

20610 

20610 

20579 

20548 

20517 

20486 

20455 

20423 

20391 

20359 

31 

127 

20326 

20294 

20261 

20228 

20195 

20161 

20128 

20094 

20060 

20026 

34 

128 

19991 

19956 

19921 

19886 

19851 

19816 

19780 

19744 

19708 

19672 

36 

129 

19635 

19598 

19561 

19524 

19487 

19449 

19412 

19374 

19335 

19297 

38 

130 

19258 

19220 

19181 

19141 

19102 

19063 

19023 

18983 

18943 

18902 

40 

131 

18862 

18821 

18780 

18739 

18697 

18656 

18614 

18572 

18530 

18488 

42 

OK 

18445 

18402 

18359 

18316 

18273 

18230 

18186 

18142 

18098 

18054 

44 

133 

18009 

17964 

17919 

17874 

17829 

17784 

17738 

17692 

17646 

17600 

46 

131 

17551 

17507 

17460 

17413 

17366 

17319 

17271 

17224 

17176 

17128 

47 

135 

17079 

17031 

1698.2 

16933 

16884 

16835 

16785 

16736 

16686 

16636 

49 

136 

16586 

16536 

16485 

16435 

16384 

16333 

16282 

16230 

16179 

16127 

51 

137 

16075 

16023 

15971 

15918 

15865 

15813 

15760 

15706 

15653 

15600 

53 

138 

15546 

15492 

15438 

15384 

15329 

15275 

15220 

15165 

15110 

15055 

55 

139 

14999 

14944 

14888 

14832 

14776 

14720 

14663 

14607 

14550 

14493 

56 

140 

14436 

14379 

14321 

14264 

14206 

14148 

14090 

14031 

13973 

13914 

58 

141 

13856 

13797 

13738 

13679 

13619 

13560 

13500 

13440 

13380 

13320 

60 

142 

13259 

13199 

13138 

13077 

130]  6 

12955 

12894 

12833 

12771 

12709 

61 

113 

9.8612617 

125H5 

12523 

12461 

12398 

12336 

12273 

12210 

12117 

12083 

-63 

1 

TABLE  XXVI. 


'•it/mi  ,,/•//„•  Elliptic  R,,,lins   V,;-t,,rJiir  BBS  =  0. 
(••Hitit.-iiit  Miliinn  -l.-.l                                          IYrit.il  tifArfjiiini'iii  1 

Arg.  I. 

ii 
0.0 

.1 
O.I 

.1 

o.a 

.1 
o.:t 

,i 

0.1 

.1 
0.5 

,i 
0.0 

.1 
0.7 

.1 

O.M 

.1 
o.  > 

war, 

H.I. 

a 

111 

9.8612030 

1  l!)5(i 

1  1893 

11829 

11765 

11701 

11636 

11573 

11507 

1  1  1  13 

-61 

146 

1  137S 

11313 

112  IS 

111N2 

11117 

11051 

I09S6      10920 

10854 

107.ss 

86 

146 

10721 

10655 

[0588 

10522 

10455 

10388 

10321 

10251 

10186 

10119 

67 

It? 

10051 

099s:f 

09916 

09s  IN 

09779 

09711 

09648 

0957  1 

09505 

09  137 

1  is 

09968 

0!)299 

09229 

09160 

09091 

09021 

08951 

08812 

OS7  11 

70 

11!) 

(Hi;:  i     (is(ioi 

08531 

()s  160 

os:is9 

08318 

08248 

Osl7ii 

08105 

71 

.       150 

07963       07S9I 

07819 

077  is 

07676 

07601      07532 

07  159 

07387 

07315 

72 

151 

07  2  12 

071ti!) 

07097 

07034 

06951 

06s 

06781 

06858 

06584 

78 

[83 

06511 

OCI37 

063<i.!      ( 

06215 

06141 

o;io;;ii 

05992 

059  17 

o.-.sn 

7  1 

15.'} 

05768 

()5(ii)3 

05(il!t      05511 

05  HiS 

o:.:i!i:i      053  is      052  13 

05167      05991 

78 

164 

05016 

01!)  10 

OIS61      0 

01712 

on;:!.;     oi5;;o    OHM 

01107 

01331 

78 

155 

04264 

01177 

04101 

0  102  1 

03947 

03870 

03793 

037  15 

03688 

03561 

77 

196 

08488 

03106 

03328 

03251 

03173 

03095 

03017 

02989 

03788 

7s 

1  57 

03701 

02626 

025  is      (' 

02390 

02312 

02283 

02151 

02075 

01997 

79 

158 

01918 

01s:!S 

0175!!      OKisO 

OKiOl 

01521 

01442 

OI3i!3 

01283 

01203 

79 

159 

01134 

010  II 

00%  1 

00884 

00804 

00784 

00644 

0!)56  1 

00484 

00103 

B8 

160 

9.8800328 

OIK!  13 

00169 

00001 

199931 

99840 

9:!759 

99678 

9959S 

81 

161 

19517 

99436 

99356 

9927  1 

9!)  193 

99  1  1  1 

99030      9 

81 

163 

98705 

9S62  1 

!)S5  12 

9S161 

98379 

98297 

98216 

98134 

9S052 

97971 

169 

97889 

97807 

97728 

97613 

97561 

97479 

97397 

97315 

97388 

97151 

N2 

161 

97088 

96986 

96904 

96739 

96657 

96678 

96192 

96110 

9632*3 

N2 

[65 

962)5      96162      !)(i!)s(l      !).-,!)«)7 

95911 

95839 

957  19 

95666 

955S  1 

95501 

88 

166 

!):>!  is     95335 

95253      1)5170 

95087 

9500  1 

91921 

9  1S3S 

94756 

91673 

98 

167 

94590 

91507 

9  1  12  1 

91311 

9I2.YS 

91175 

9  1092 

91009 

93926 

98848 

S3 

188 

93760 

93(577 

9359  1 

93510 

93127 

93344 

98361 

98111 

98098 

93012 

169 

92999 

92si6 

92768 

92679 

92591  i 

92513 

92  130 

923  17 

9226  1 

921S1 

S3 

170 

92098 

92()i:> 

91932 

91848 

91765 

91689 

91599 

91516 

91133 

91350 

171 

91267 

911H1 

91101 

91018 

90935 

90852 

90769 

90686 

90603 

90521 

83 

172 

90  i:is 

90355 

90272 

90189 

90106 

90021 

89941 

89858 

S9775 

S9S93 

17:} 

89610 

89527 

S9115     S9362 

89280 

89197 

89115 

WMI32 

88950 

88867 

N3 

171 

887s:> 

88702 

88620 

sv;,:;s 

88456 

88373 

88291 

88209 

88127 

SS015 

N2 

175 

87963 

S7ssi 

87798 

87717 

N7635 

87558 

87471 

87308 

87226 

82 

176 

87111 

87063 

86981 

86900 

86818 

86737 

86698 

86574 

86498 

SCI  12 

81 

177 

86330 

N62  1!) 

86168 

86087 

86006 

85925 

S5S  I  1 

85768 

85602 

si 

178 

85521 

S5  1  1  1 

85360     S52SO 

85199 

85119 

85039 

si:  159 

84878 

84798 

SO 

179 

84718 

N163S 

S155S 

84478 

S1399 

81319 

8  1239 

si  159 

84080 

81000 

NO 

180 

83921 

s:;^  i-j 

88769 

83683 

83601 

88538 

S3  116 

83367 

88988 

H32K) 

79 

181 

83131 

83052 

8297  1 

82895 

S2S17 

82739 

S2661 

82589 

N250  1 

N2  126 

7s 

182 

823  is 

82271 

82193 

82115 

82038 

81960 

81883 

81806 

81728 

81651 

77 

183 

81574 

81497 

81121 

81844 

81267 

81190 

BUM 

81038 

80961 

suss;, 

77 

184 

80809 

S0733 

80657 

80581 

80505 

SO  130 

80894 

80378 

80968 

80128 

76 

185 

80053 

79978 

79903      79S2S 

79788 

79878 

79601      79529 

7!)  155 

79381 

75 

186 

79307 

79233 

79159     7!«)S5 

79011 

78938 

7ssii|      7S791 

78717 

7S6  1  1 

71 

187 

78571 

78496 

78426 

78868 

78280 

78208 

78188 

78083 

77991 

77919 

72 

iss 

778  17 

77775 

7770  1 

77689 

77561 

77489 

77418 

77317 

77276 

77908 

71 

189 

771:55     "Oil 

7699  1      76923 

76853 

76718 

76843 

7657  1 

76501 

70 

190 

76135      7i;::ii5 

76296      76227 

76158 

76090 

76021 

75952 

75884 

758HJ 

89 

191 

9.85757  is      756sO      75312      75511 

75  177 

75  109 

75312 

75278 

76308 

75111 

—67 

TABLE  XXVI. 


Logarithm  of  the  Elliptic  Radius  Vector  for  SBI  =  0. 

Constant  subtracted  0.0000257.        Period  of  Argument  I.  224''  .7008. 

a 

(i 

d 

ii 

a 

d 

d 

d 

a 

d 

Arg.  I. 

0.0 

0.1 

0.2 

0.3 

0.4 

0.5 

O.6 

0.7 

0.8 

O.9 

L)iff. 

for  Od.1. 

a 

102 

9.8575074 

75008 

74941 

74875 

74809 

7  17  13 

'  74677 

74611 

74545 

74480 

-66 

193 

74115 

74350 

74285 

74220 

74155 

74090 

74026 

73962 

73898 

73834 

64 

194 

73770 

73706 

73643 

73579 

73516 

73  153 

73390 

73327 

73265 

73202 

63 

195 

73140 

73078 

73016 

72951 

72893 

72831" 

72770 

72709 

72648 

72587 

61 

196 

72526 

72465 

72405 

72315 

72285 

72225 

72165 

72103 

72046 

71987 

60 

197 

71928 

718G9 

71810 

71752 

71693 

71635 

71577 

71519 

71462 

71101 

58 

198 

71317 

71289 

71232 

71175 

71119 

71062 

71006 

70950 

70894 

70838 

56 

199 

70782 

70727 

70671 

70316 

70561 

70507 

70152 

70398 

70343 

70289 

55 

200 

70236 

70182 

70128 

70075 

70022 

69969 

69916 

69863 

69811 

69759 

53 

201 

C9707 

69655 

69603 

69552 

69500 

69449 

69398 

69317 

69297 

69246 

51 

202 

69196 

69116 

69096 

69047 

69899 

68948 

68899 

68850 

68801 

68753 

49 

203 

68705 

68657 

68609 

68561 

68514 

68166 

68419 

68372 

68326 

68279 

47 

204 

68233 

68186 

68140 

68095 

68049 

68004 

67959 

67914 

67869 

67824 

45 

205 

67780 

67736 

67692 

67648 

67605 

67561 

67518 

67475 

67432 

67390 

43 

206 

67317 

67305 

67263 

67222 

67180 

67139 

67098 

67057 

67016 

66975 

41 

207 

66935 

66895 

66855 

66815 

66776 

66737 

66698 

66659 

66620 

66582 

39. 

208 

685  1  1 

63506 

66468 

66130 

66393 

66356 

66319 

66282 

66246 

66209 

37 

209 

66173 

66137 

66102 

66066 

66031 

65996 

65961 

65927 

65892 

65858 

35 

210 

65824 

65790 

65757 

6572  1 

65690 

65658 

65625 

65592 

65560 

65528 

33 

211 

65496 

65465 

65434 

65403 

65372 

65341 

65310 

65280 

G5250 

65220 

31 

212 

65191 

65162 

65133 

65101 

65075 

65016 

65018 

64990 

64962 

64935 

28 

213 

64907 

64880 

64853 

61827 

64800 

61771 

61718 

61722 

64697 

64672 

26 

214 

64646 

64622 

64597 

64573 

64548 

64524 

64501 

61477 

64454 

64431 

24 

215 

64408 

64385 

64363 

64311 

64319 

64297 

61276 

61255 

64234 

64213 

22 

216 

61192 

64172 

64152 

64132 

64112 

64093 

64074 

64055 

64036 

64018 

19 

217 

63999 

63981 

63964 

63946 

63929 

63912 

63895 

63878 

63862 

63846 

17 

218 

63830 

63814 

63799 

6378  I 

63769 

63754 

63739 

63725 

63711 

63697 

15 

219 

63684 

63670 

63657 

63611 

63632 

63619 

63607 

63595 

63584 

63572 

12 

220 

63561 

63550 

63539 

63528 

63518 

63508 

63498 

63489 

63179 

63170 

10 

221 

63161 

63  153 

63  1  i  I 

63136 

63428 

63420 

63113 

63406 

63399 

63392 

8 

222 

63386 

63379 

63373 

63367 

63362 

63357 

63351 

63317 

63312 

63338 

5 

223 

63333 

63330 

63326 

63322 

63319 

63316 

63314 

63311 

63309 

63307 

3 

224 

9.8563305 

63303 

63302 

63301 

63300 

63300 

63299 

63299 

63299 

63300 

-  o 

TABLE  XXVII. 


51 

TAII1YE  X\VIII. 


*,,«,/„„/„„  of  Log.  r.. 

Prrt.  of  lag.  r. 

F:irtor  tn  lie  multiplied  by  111,  and  its  lun.-irithm.                  I'.-riuil  i.l"  Ar<-iiiin-iit  1.  =  I 

Fact,  to  be  X  (  ™)2 

Arg.I 

Fartiir. 

In;;,  I'll- 

Ar^.l      F.-irti.r.      i 

Factor.     1 

Arg.I 

.    Factor 

,og.fac 

Arg.I. 

Factor. 

d 

0 

+  13  15 

1   12- 

d 

(il 

-   Mil 

d 

-1946    .,1  II  3-. 

l-i 

+  4.06 

06I-: 

d 
0 

-2.1 

1 

13.45 

1.12* 

1,1 

1.07 

121 

12.90 

I.I  IOC 

l-l 

1  II 

iii.ll: 

4 

2.1 

8 

1343 

1.1961 

62 

2:11 

0.36.K 

122         12-1 

1  1071 

1-2 

477 

0.67-  i 

8 

2.0 

3 

I::  |.i 

1.1272 

63 

271 

0.4395 

123 

1271 

1   |o| 

1-.: 

.'.  12 

0.709: 

12 

20 

•    4 

+13.36 

1.1960 

1,1 

-  3.07 

n'l  1-71 

121 

-125!) 

•1.1009 

l-l 

+  5.17 

07377 

16 

-l.il 

."> 

1  3.32 

1  .  1  2  1  1 

3.13       i 

1  25 

12  1*       1  H9(,l 

165 

.">  -1 

n  7i,l2 

1  - 

6 

13.26 

1  .  1  22  1 

66 

0.57-1 

196 

12:15        1.0015 

l-t, 

1,  15 

0.7868 

24 

1.6 

7 

i::  10 

1.  12.11 

SI 

4.14 

H.6I72 

127 

1221 

1-7 

'     1- 

o.-n- 

1  --, 

8 

+  13.10 

1  1171 

6- 

-    1   19 

12* 

-12   fi 

•14818 

186 

04333 

32 

-1.3 

0 

13.01 

1.1144 

i,  ' 

l-l 

n  (.-17 

1  2:  i 

ll.oo      ; 

169 

7.13 

36 

I.I 

10 

19.91 

linn 

7  i 

5.1* 

o.7l  II 

130 

1171 

1  litiOl, 

100 

7  15 

n  -723 

lo 

0.9 

11 

12-0 

1.1072 

71 

"7110 

131 

1  1  .56 

1.0630 

101 

7.77 

II 

0.7 

12 

+  12.6-1 

1.1030 

72 

-   5  -.-> 

•9.7674 

138 

II    '- 

,,1.0561 

199 

4*. 

-  0.5 

13 

12.54 

1.0984 

73 

6.1*       0.7012 

133 

11.10       l.til-7 

103 

0.9229 

Da 

-0.2 

14 

12  ID 

1.0935 

74 

651 

0.8134 

134 

1.0408 

194 

0.937!) 

56 

0.0 

10 

12.25 

14880 

75 

6.83 

04348 

135 

10.77 

L4394 

196 

8.95 

84390 

60 

+  0.2 

16 

+  120* 

1  H-22 

76 

-  7.14 

136 

-1056 

•14836 

196 

+  0.23 

0.9653 

64 

+  0.5 

17 

II  .01 

1.0760 

77 

7  15 

04790 

137 

10.33 

1  <il  II 

107 

941 

0.9780 

68 

0.7 

18 

11.73 

1.0693 

7- 

7.75 

138 

10.10 

1,0041 

19* 

977 

0.9699 

72 

0.9 

10 

1  1  .5  1 

1  nt  ,22 

79 

8.05 

04056 

130 

9-  , 

10!) 

10.03 

1.0013 

76  • 

1.1 

20 

+11.34 

14546 

80 

-  8.33 

140 

-  9.60 

•04635 

200 

+10.28 

1.0119 

80 

+  1.3 

21 

11.13 

1  .0465 

81 

-1,2 

0.9364 

III 

0.35 

0.9707 

801 

1049 

l  0990 

84 

15 

22 

10.91 

1.037!) 

n 

8.8!) 

11.0191 

1  12 

0.9583 

809 

10.75 

1.0315 

88 

1  Ii 

23 

10.6* 

1  '2-7 

83 

0.16 

0.9621 

113 

8.81 

04451 

1048 

1.0405 

92 

1.8 

21 

+10.15 

i  mm 

84 

-  9.43 

•04749 

1  II 

HI).!  13  II 

204 

+11.1!) 

14480 

96 

+  1.9 

25 

10.21 

1  0068 

83 

0.6* 

115 

04164 

II    ID 

1.0560 

100 

2.0 

96 

045 

0.9979 

BO 

0.03 

1  In 

746 

0.900* 

1161 

1.0644 

104 

2.0 

9.69 

0.9-61 

87 

10.17 

1.0079 

1  17 

7.61, 

0.8842 

207 

11.79 

i  on  i 

108 

2.1 

98 

+  9.13 

04743 

88 

-10.40 

«  1.0  I/O 

148 

-  7.36 

+11.96 

1.0779 

112 

+  21 

80 

0.15 

ii  961  1 

89 

1062 

1  n2i,2 

149 

7.05 

0.8480 

200 

12  13 

1.0640 

116 

2.1 

8.87 

0.917* 

Oil 

lo-l 

1.031!) 

150 

6.73 

n  -2-1 

210 

1220 

l  08  '7 

120 

2.0 

31 

8.58 

0.9335 

91 

11.05 

1.0432 

151 

6.41 

211 

12  II 

1.0950 

I'M 

2.0 

M 

+  8.28 

0.91-2 

92 

-1  1  .24 

n  1.0509 

I.VJ 

-  6.08 

•07849 

212 

(.18.58 

1  0000 

12* 

+  1.9 

33 

746 

09  121 

03 

11,13 

I.058S1 

153 

5.7:, 

813 

1271 

1.1043 

139 

I.K 

31 

7.67 

n  --  ,  l 

M 

11.61 

1.0650 

151 

5.  12 

0.733!) 

214 

19.83 

110-3 

136 

1.7 

35 

7.36 

0.8668 

05 

11.79 

1.0714 

l.V, 

5.08 

n.7'  l.V.  ' 

846 

1844 

1  1120 

up 

1.5 

M 

+  7.04 

03476 

96 

-11.!  15 

itl.  0774 

156 

-  4.73 

nO.6753 

216 

+  13.01 

1  1153 

144 

+  1.3 

6.71 

0.8270 

07 

12.10 

1.0630 

157 

4.30 

'  n,  122 

217 

13.13 

1.11*3 

1  I-' 

I.I 

38 

6.38 

04051 

0* 

1  2.25 

l  0661 

158 

I'll 

0.6059 

21* 

13.21 

1  1908 

152 

0.9 

30 

6.05 

0.7816 

90 

12.3:) 

14030 

159 

3.68 

0.5660 

210 

13.2* 

1.1831 

156 

0.7 

40 

+  5.71 

0.7565 

100 

-1251 

n  1.0074 

160 

-  3.32 

•04818 

220 

+13.33 

1  121' 

160 

+  0.5 

41 

5.36 

0.7206 

101 

1263 

Moll 

161 

2.% 

0.4716 

221 

13.3* 

I.I  261 

164 

0.3 

42 

549 

0.7004 

102 

18.74 

1.1050 

162 

2.60 

0.4146 

899 

13  II 

1.1275 

168 

+  0.0 

13 

4.66 

061,*- 

103 

12.83 

1.1083 

163 

2.23 

0.3487 

223 

13.11 

1.12*3 

172 

-  0.2 

II 

+  4.31 

0.6314 

till 

-1849 

nl.1113 

161 

-   l-t, 

,,0.2707 

22  1 

+  13.15 

1  12-7 

176 

-0.4 

45 

3.95 

0.5966 

105 

13.00 

I.I  139 

165 

1  .10 

0.1746 

05 

13  15 

1  12- 

l-  i 

0.7 

46 

:(.vi 

0.5550 

106 

13.07 

1  1162 

166 

1.12 

0.0511 

226 

13    II 

1  12-5 

1*1 

0.0 

47 

3.22 

04065 

107 

13.13 

f.iiaa 

167 

0.75 

9.  -7i,2 

2-27 

13  12 

1.1970 

188 

1.1 

48 

+  2.*6 

0.4589 

108 

-13.17 

nl  119* 

168 

-  0.38 

•94766 

22- 

+13.30 

1.1260 

109 

-  1.3 

49 

0.3061 

100 

13.21 

1.1210 

16!) 

-  0.01 

n".7*53 

220 

13.35 

1.1956 

l!Hi 

15 

50 

2  12 

0.3265 

110 

3.21 

1.1990 

170 

+  0.37 

/(0.565* 

230 

13.30 

1.1239 

888 

1  Ii 

51 

1.75 

0.2430 

III 

3.26 

1.1225 

171 

0.74 

94704 

231 

1344 

1  121* 

2  il 

14 

52 

1  3* 

O.I  3*0 

112 

-  3.27 

nl.l2iW 

172 

+  1  12 

0.0177 

838 

+  13.17 

1.1193 

20- 

-  1.9 

l.oo 

0.0017 

113 

3.27 

1  1  22* 

173 

1.4!) 

0.1726 

233 

I3.0S 

I.I  165 

212 

2.0 

54 

0.63 

0.7993 

114 

3.26 

1  1221 

171 

146 

. 

2:u 

1949 

II  131 

216 

20 

+  0.20 

,9.10-2 

115 

13.23 

1.1217 

175 

2.23 

04489 

•J35 

12.88 

1.1099 

220 

2.1 

-  0.12 

00719 

116 

-13.20 

»  1  .  1  2  '7 

176 

+  2.60 

0  .1151 

886 

+12.77 

1.1060 

221 

-21 

57 

0.19 

9.6:i|  | 

117 

13.16 

1.1  193 

177 

2.07 

0.  172.', 

2:17 

121,1 

1.1017 

22- 

21 

KU 

0.-6 

0.036  1 

118 

13.11 

1.1176 

17* 

3.33 

0.523  1 

238 

125  i 

1.0070 

839 

2  1 

«JO 
r.ii 

0.0017 

1  Ml 

13.05 

I.I  156 

170 

3.70 

0.56*  l 

I2:u; 

1.0919 

2:!6 

2.0 

.1.  ' 

6) 

1  tM 

nO.2057 

190 

-12.98 

n  1.1  132 

18.) 

+  4.06 

211 

+  12.20 

1-0-63 

210 

-  1.0 

11'  V 


The  purtiirbationu  are  in  units  of  the  eighth  decimal  place 


TABLE   XXIX. 


Perturbations  of  Log.  r,  by  the  Earl/i. 

Constant  added  1594.             Period  of  Argument  VI.,  583d  .92. 

Arg.  VI. 

Equa. 

Arg.  VI. 

Equa. 

Arg.  VI. 

Equa. 

Arg.  VI. 

Equa. 

Arg.  VI. 

Equa. 

Arg.  VI.   Equa. 

<t 

d 

d 

d 

d 

d 

0 

1716 

104 

185!) 

808 

550 

312 

2856 

416 

45 

520 

2527 

2 

718 

106 

1795 

210      614 

314 

2811 

418      64 

Bia 

2524 

4 

725 

108 

1  72!) 

212  '    681 

316 

2762 

420      87 

524 

2518 

6 

736 

110 

1662 

214 

751 

318 

2709 

422     111 

526 

2509 

8 

751 

112 

1593 

216 

829 

320 

2653 

424      1-15 

528 

2496 

ID 

769 

114 

I5SKJ 

218 

896 

322 

25!  14 

426 

179 

530 

2480 

12 

792 

116 

1452 

220 

972 

324 

2531 

428 

216 

532 

2460 

14 

1818 

118 

1381 

2aa 

1049 

326 

2466 

430 

258 

534 

2438 

16 

1846 

120 

1310 

221 

1128 

328 

2397 

432 

302 

536 

2413 

18 

1878 

122 

1238 

226 

1209 

330 

2326 

434 

350 

538 

2385 

20 

1912 

124 

1166 

228 

1290 

332 

2253 

436 

401 

540 

2356 

22 

1948 

196 

10!  15 

230 

1372 

334 

2178 

438 

454 

542 

2323 

24 

1985 

128 

1024 

232 

1455 

336 

2101 

440 

510 

544 

2289 

26 

2(124 

130 

955 

234 

1538 

338 

2022 

442 

569 

546 

2253 

a8 

2064 

132 

886 

236 

1621 

340 

1942 

444 

620 

548 

2216   . 

30 

2103 

134 

818 

238 

1704 

342 

1861 

446 

692 

550 

2177 

32 

21i:i 

136 

752 

240 

1787 

344 

1780 

448 

757 

552 

2138 

34 

2183 

138 

687 

242 

1869 

346 

1697 

450 

823 

554 

2098 

36 

2221 

140 

624 

244 

1950 

348 

1614 

452 

891 

556 

2059 

38 

2259 

149 

563 

246 

2030 

350 

1531 

454 

960 

558 

2019 

40 

22!  14 

144 

505 

248 

2108 

352 

1448 

456 

1029 

560 

1981 

42 

2:32!) 

146 

449 

250 

2185 

354 

1365 

458 

1100 

562 

1944 

44 

2361 

148 

3!  15 

252 

2260 

356 

1283 

460 

1171 

564 

1908 

46 

2391 

150 

345 

254 

2333 

358 

1202 

462 

1243 

566 

1874 

48 

2418 

152 

297 

256 

2404 

360 

1123 

464 

1315 

568 

1843 

50 

2443 

154 

253 

258 

2472 

362 

1044 

466 

1386 

570 

1814 

52 

2465 

156 

212 

260 

8538 

364 

967 

468 

1457 

572 

178!) 

54 

2484 

158 

174 

262 

2600 

366 

891 

470 

1528 

574 

1767 

56 

2500 

160 

140 

264 

265!) 

368 

818 

472 

1598 

576 

1749 

58 

2513 

162 

109 

266 

2715 

370 

746 

474 

1666 

578 

1734 

60 

2522 

164 

83 

268 

2767 

372 

677 

476 

1733 

580 

1724 

62 

2528 

166 

60 

270 

2815 

374 

610 

478 

17!  19 

•  582 

1718 

64 

2531 

168 

41 

272 

i860 

376 

516 

480 

1863 

584 

1716 

66 

2530 

170 

27 

274 

2901 

378 

485 

482 

1924 

586 

1718 

68 

2525 

172 

17 

276 

2938 

380 

427 

484 

1984 

588 

1725 

70 

2517 

174 

11 

278 

2970 

382 

372 

486 

2041 

590 

1737 

72 

2505 

176 

9 

280 

2999 

384 

321 

488 

2095 

592 

1752 

74 

2490 

178 

12 

282 

3023 

386 

273 

490 

2147 

594 

1770 

76 

2471 

180 

19 

284 

3043 

388 

22!) 

492 

2196 

596 

1793 

78 

2449 

182 

31 

286 

3058 

390 

188 

494 

2242 

598 

1819 

80 

2423 

184 

46 

288 

3069 

303 

152 

496 

2285 

600 

1847 

82 

2393 

186 

66 

290 

3076 

394 

119 

498 

2324 

61)2 

187!) 

84 

2360 

188 

91 

299 

3078 

396 

91 

500 

2361 

604 

1913 

86 

2323 

190 

120 

294 

3075 

398 

67 

502 

2393 

606 

1950 

88 

2284 

192 

153 

296 

3068 

400 

47 

504 

2422 

608 

1987 

90 

2241 

194 

189 

298 

3057 

402 

32 

506 

2448 

610 

2026 

92 

2194 

196 

230 

300 

3041 

404 

20 

508 

2470 

612 

2066 

94 

2145 

198 

275 

302 

3820 

406 

14 

510 

2489 

614 

2105 

96 

2093 

200 

323 

304 

8996 

408 

11 

512 

2503 

616 

2145 

98 

2039 

202 

375 

306 

2!  167 

410 

13 

514 

2515 

618 

2185 

100 

1981 

204 

430 

308 

2934 

412 

20 

516 

2523 

620 

2223 

102 

1921 

206 

488 

310 

2897 

414 

30 

518 

2527 

622 

2261 

101 

1850 

208 

550 

312 

2856 

416 

45 

520 

2527 

624 

2295 

The  perturbations  are  in  units  of  the  eighth  decimal  place. 

TABLES. 


TVHM:  xxx. 

TIUI.I:  v\\i. 

1'rrtiirlnitioii.t  ii  f  /.cif.  r,  lif  tin-  AW///. 

Perturbations  «i'  /<»;,'.  /•,  l>y  ./»//(/•/•. 

ronMaiitail.k.l  Hi-.'.     Period  oflrg.  \  II.  -.M 

('uiiMaiil  a<lil<-il    11  .                IVriuJ  at  \i(_.  I.X.,  •.>:!!»•'  .99. 

Arg.  \  1  1 

1 

tit    Ml 

l'.c|ll;i. 

Arp  IX. 

l'.<|iia. 

Lq  l\ 

Ki|ila 

Arg   l\ 

I)||1KI. 

1 

.1 

d 

.1 

d 

II 

171 

198 

I'D 

0 

80 

8n 

H,  1 

368 

4 

154 

139 

l!>7 

1 

585 

-J 

169 

380 

- 

IS7 

196 

SI3 

4 

586 

-1 

n>i 

III 

Ii 

I-JI 

140 

-.".'- 

(i 

588 

•.'n 

166 

16 

106 

III 

M3 

8 

691 

88 

919 

H.- 

Ii,  -J 

•-'IP 

m 

146 

•J  .7 

III 

594 

BO 

194 

170 

l-l 

•Jl 

7."i 

in 

'.'TO 

19 

09 

171 

179 

U 

(il 

158 

tea 

14 

603 

M 

II- 

171 

586 

39 

1!' 

160 

893 

III 

06 

187 

176 

546 

36 

:t7 

nil 

3M 

ia 

613 

08 

106 

178 

663 

•in 

Iff 

168 

310 

90 

618 

100 

-- 

180 

570 

14 

in 

179 

316 

99 

683 

189 

71 

189 

598 

48 

19 

176 

390 

690 

104 

55 

l-l 

606 

N 

6 

180 

393 

96 

6:t:t 

106 

41 

l-i, 

617 

66 

9 

184 

394 

28 

638 

108 

2!l 

188 

627 

GO 

0 

188 

80 

(,!•.' 

110 

111 

198 

686 

M 

0 

199 

891 

645 

112 

12 

199 

641 

(:- 

1 

1<I6 

317 

34 

647 

114 

6 

194 

646 

79 

4 

200 

311 

36 

648 

iia 

•• 

1% 

649 

?6 

8 

204 

804 

38 

Btt 

118 

1 

198 

651 

80 

IS 

208 

BUB 

40 

647 

190 

1 

900 

651 

84 

93 

212 

985 

42 

644 

199 

4 

909 

651 

8« 

n 

216 

283 

44 

640 

UN 

9 

204 

649 

BB 

43 

220 

261 

46 

686 

126 

16 

L>IMi 

646 

96 

56 

224 

247 

48 

628 

128 

96 

208 

642 

100 

89 

2-.W 

989 

.-,(1 

61!) 

130 

36 

910 

IM 

83 

999 

216 

52 

188 

•I'.i 

919 

683 

in- 

98 

236 

200 

54 

596 

134 

64 

914 

628 

112 

111 

240 

184 

56 

583 

136 

81 

216 

693 

116 

130 

914 

11,7 

58 

567 

138 

90 

218 

617 

istt 

146 

•Ji- 

151 

60 

561 

140 

118 

990 

619 

124 

161 

252 

134 

89 

889 

142 

13!) 

891 

6U7 

1W 

180 

256 

118 

64 

513 

144 

169 

224 

•  >•  ,i 

602 

R4V9 

66 
68 

4!)2 
470 

146 
148 

i  ~  > 

2ll!l 

«o 
998 

.>.'/ 

508 

70 

447 

150 

234 

230 

590 

72 

423 

152 

958 

989 

588 

74 

398 

164 

285 

234 

586 

76 

373 

168 

:m 

936 

:,-:, 

78 

347 

158 

337 

938 

588 

80 

321 

160 

363 

•Jin 

586 

'I'!.'-  perturbationi)  are  in  units  oflhc  eighth  decimal  place. 

TABLE    XXXII. 


Pcrturliitionn  of  Lu<;.  /•,  Inj  M-n-ury. 

Horizontal  Argument  =  I. 

Consluiit  added  34.             IVnotI  <if  Argument  I.,  224''.7. 

<i 

d 

d      d 

.1 

d  }    d 

.1 

,i 

,1 

ii 

,i 

d       <i 

d 

Arg.X. 

0 

8 

16 

24 

32 

40 

43 

56 

61 

72 

§0 

88 

96 

104 

112 

0 

18 

21 

30 

39 

45 

44 

40 

36 

34 

35 

36 

34 

28 

23 

23 

1 

19 

24 

32 

41 

45 

43 

38 

34 

34 

35 

37 

31 

29 

25 

•27 

9 

20 

25 

-34 

42 

44 

41 

36 

33 

33 

35 

37 

35 

30 

27 

31 

3 

21 

27 

36 

42 

43 

39 

34 

33 

33 

36 

38 

35 

31 

30 

36 

4 

21 

28 

37 

42 

42 

37 

32 

31 

34 

37 

39 

36 

33 

34 

42 

5 

2-2 

2!) 

37 

41 

39 

34 

30 

31 

34 

38 

40 

37 

35 

38 

48 

6 

98 

30 

37 

40 

37 

32 

29 

31 

35 

39 

41 

39 

38 

42 

53 

7 

22 

30 

36 

38 

34 

30 

29 

32 

37 

40 

42 

41 

41 

46 

58 

8 

22 

30 

36 

36 

aa 

28 

28 

33 

39 

42 

44 

43 

44 

51 

63 

9 

22 

30 

34 

34 

30- 

27 

29 

35 

41 

44 

45 

45 

47 

55 

67 

10 

22 

29 

33 

32 

28 

27 

30 

37 

43 

46 

47 

47 

51 

59 

70 

11 

22 

29 

32 

30 

27 

27 

32 

39 

45 

48 

48 

49 

54 

63 

7-2 

12 

22 

29 

31 

29 

27 

28 

34 

42 

48 

50 

50 

->•> 

57 

66 

74 

13 

23 

30 

31 

2!) 

27 

30 

37 

45 

50 

52 

51 

54 

59 

68 

75 

14 

25 

30 

31 

29 

28 

33 

41 

49 

53 

53 

53 

56 

61 

69 

75 

15 

26 

31 

31 

29 

30 

36 

45 

52 

55 

55 

54 

58 

69 

69 

73 

16 

28 

32 

32 

31 

33 

40 

49 

55 

57 

56 

55 

59 

64 

69 

71 

17 

31 

34 

34 

33 

37 

44 

53 

58 

59 

57 

56 

59 

65 

68 

6^ 

J8 

34 

36 

36  x 

36 

41 

49 

57 

61 

61 

58 

56 

60 

65 

67 

65 

1!) 

38 

39 

38 

40 

45 

54 

61 

63 

62 

58 

57 

6J 

64 

65 

61 

20 

42 

42 

42 

44 

50 

59 

64 

65 

62 

58 

57 

63 

63 

62 

56 

21 

46 

46 

45 

48 

55 

63 

68 

66 

62 

57 

57 

59 

61 

59 

51 

22 

50 

50 

50 

53 

60 

67 

70 

67 

62 

57 

56 

59 

59 

55 

47 

23 

55 

53 

54 

58 

65 

71 

71 

67 

61 

56 

55 

58 

57 

51 

42 

24 

59 

57 

58 

63 

69 

73 

72 

66 

59 

55 

54 

56 

54 

47 

38 

25 

63 

61 

62 

67 

73 

75 

72 

64 

57 

54 

53 

54 

51 

43 

35 

26 

67 

65 

66 

71 

75 

76 

71 

62 

55 

52 

52 

51 

47 

39 

32 

27 

70 

68 

70 

74 

77 

76 

69 

60 

53 

50 

51 

49 

44 

36 

30 

28 

73 

71 

73 

76 

78 

75 

66 

57 

51 

48 

49 

47 

41 

34 

28 

29 

75 

73 

75 

78 

78 

72 

63 

54 

48 

46 

47 

45 

38 

32 

27 

30 

76 

75 

76 

78 

76 

69 

59 

50 

45 

44 

45 

42 

36 

30 

27 

31 

77 

75 

77 

77 

74 

65 

55 

46 

42 

42 

44 

40 

34 

29 

28 

32 

77 

75 

76 

75 

70 

60 

50 

42 

40 

41 

42 

38 

33 

29 

29 

33 

75 

74 

71 

72 

66 

55 

45 

38 

38 

39 

41 

36 

32 

29 

31 

34 

73 

72 

72 

69 

63 

49 

40 

35 

36 

38 

39 

35 

31 

30 

33 

35 

71 

69 

68 

64 

54 

44 

35 

32 

34 

37 

38 

35 

31 

31 

35 

36 

67 

66 

64 

58 

48 

38 

31 

30 

33 

36 

37 

34 

31 

32 

38" 

37 

63 

62 

59 

52 

42 

32 

26 

28 

32 

36 

36 

34 

32 

34 

40 

sa 

58 

57 

53 

46 

35 

27 

23 

26 

31 

35 

35 

33 

33 

36 

43 

39 

53 

52 

47 

39 

M 

22 

21 

25 

31 

34 

34 

33 

34 

38 

45 

40 

48 

46 

41 

32 

23 

18 

19 

25 

31 

34 

34 

33 

35 

40 

46 

41 

42 

40 

35 

26 

18 

15 

18 

25 

32 

34 

34 

34 

36 

41 

46 

42 

37 

35 

29 

2!) 

14 

13 

17 

25 

33 

35 

34 

35 

38 

42 

46 

43 

32 

2!) 

23 

15 

10 

11 

18 

26 

33 

35 

34 

35 

39 

43 

45 

44 

27 

24 

18 

11 

.8 

11 

19 

28 

34 

35 

34 

36 

40 

43 

44 

45 

23 

19 

13 

7 

6 

12 

21 

30 

35 

36 

35 

36 

40 

42 

42 

46 

19 

15 

9 

5 

6 

13 

23 

32 

36 

36 

35 

37 

41 

42 

40 

47 

15 

19 

6 

4 

7 

15 

25 

34 

37 

36 

35 

37 

41 

41 

37 

48 

13 

9 

4 

3 

8 

18 

28 

39 

38 

37 

35 

38 

41 

40 

34 

49 

11 

7 

3 

4 

11 

21 

31 

37 

38 

37 

36 

38 

40 

38 

31 

50 

9 

5 

3 

5 

14 

25 

34 

39 

39 

37 

36 

38 

39 

35 

27 

51 

8 

5 

4 

8 

17 

29 

37 

40 

39 

37 

36 

38 

38 

32 

24 

52 

8 

5 

5 

II 

21 

32 

39 

41 

39 

37 

36 

38 

37 

30 

21 

53 

9 

6 

7 

II 

25 

36 

41 

41 

39 

37 

36 

37 

36 

28 

18 

54 

9 

7 

10 

18 

39 

39 

43 

41 

38 

36 

36 

37 

34 

26 

16 

55 

10 

9 

13 

22 

33 

41 

44 

40 

38 

36 

36 

36 

32 

24 

15 

56 

12 

12 

17 

26 

37 

43 

44 

40 

37 

35 

36 

35 

31 

83 

15 

57 

13 

14 

20 

30 

40 

45 

44 

39 

30 

35 

36 

35 

30 

21 

16 

58 

15 

10 

24 

34 

42 

45 

43 

38 

35 

35 

36 

34 

29 

21 

17 

59 

16 

19 

27 

37 

44 

45 

42 

37 

34 

35 

36 

34 

28 

22 

1!) 

60 

18 

21 

30 

39 

45 

44 

40 

36 

3-1 

35 

36 

34 

28 

23 

93 

The  perturbations  an.'  in  units  of  the  eighth  decimal  plncu. 


TAKLK    XXXII. 


r<-rliirl>iiti<nix  (>/'  /„(>«,'.  r,  /<//  Mi'rriiry. 

Ilixi/.'HiUl  Ar^iniii'iit  =  I. 

Const  ml  ;nlc|.-il  ill.                             IVriod  c.l'Ar-ii  nl  X  ,  >',)  units. 

Arg.  X. 

» 
120 

,i 
1!IN 

.1 

i:t<> 

111 

.1 
1  •->•.> 

K.;> 

.1 

1«M 

17« 

.1 
IW1 

i»a 

aoo 

t 

aow 

an« 

.1 

aai 

,\ 
a:w 

0 

87 

37 

i- 

68 

60 

65 

7:, 

03 

04 

88 

-i 

7.-. 

71 

1 

33 

II 

55 

60 

63 

(,-, 

71 

81 

:M 

06 

03 

79 

73 

79 

a 

30 

51 

61 

65 

67 

7  i 

76 

1)3 

06 

09 

7.-, 

70 

60 

3 

45 

57 

66 

60 

71 

7:1 

7J 

88 

05 

06 

7:' 

71 

66 

(,:, 

4 

69 

63 

71 

73 

71 

76 

-J 

DO 

06 

03 

85 

71 

66 

69 

61 

B 

58 

71 

7.-, 

71  i 

78 

-1 

91 

03 

HO 

61 

57 

56 

6 

til 

7:s 

77 

77 

77 

78 

00 

90 

-l 

73 

69 

55 

59 

7 

68 

76 

78 

78 

77 

70 

B6 

88 

7- 

66 

10 

47 

44 

- 

79 

78 

7:i 

77 

76 

70 

83 

85 

80 

711 

48 

43 

41 

:!'.i 

!• 

78 

79 

7!l 

7.-, 

74 

77 

80 

80 

73 

69 

r,n 

41 

37 

:«i 

as 

Ill 

77 

79 

77 

73 

72 

74 

76 

71 

66 

54 

19 

34 

31 

31 

•-•- 

II 

78 

78 

74 

7(1 

611 

71 

72 

68 

45 

34 

•j- 

96 

83 

19 

7- 

7.-. 

70 

66 

65 

67 

67 

61 

50 

:c 

97 

22 

23 

89 

19 

13 

77 

79 

66 

69 

61 

69 

61 

53 

49 

89 

.'I 

17 

18 

18 

15 

14 

74 

68 

61 

57 

57 

57 

55 

46 

34 

22 

15 

13 

IB 

16 

11 

16 

70 

63 

57 

53 

53 

52 

49 

39 

27 

16 

10 

10 

13 

19 

9 

16 

66 

58 

69 

48 

49 

l- 

42 

39 

20 

10 

7 

8 

11 

10 

7 

17 

61 

63 

47 

44 

45 

43 

36 

26 

14 

6 

5 

7 

10 

10 

6 

18 

66 

48 

42 

40 

41 

38 

31 

80 

9 

3 

4 

7 

10 

9 

5 

19 

61 

43 

38 

37 

37 

34 

96 

15 

5 

2 

3 

8 

10 

9 

6 

20 

46 

38 

34 

34 

34 

30 

21 

11 

3 

1 

4 

9 

11 

9 

7 

Bl 

41 

:M 

39 

39 

32 

87 

17 

8 

2 

1 

6 

11 

19 

10 

8 

89 

37 

31 

30 

31 

30 

24 

15 

6 

2 

3 

!» 

13 

13 

11 

10 

93 

33 

28 

99 

30 

28 

99 

13 

6 

3 

6 

19 

15 

14 

19 

19 

24 

30 

26 

28 

21) 

27 

21 

12 

6 

5 

9 

14 

17 

16 

14 

14 

to 

98 

26 

28 

30 

27 

20 

12 

7 

7 

12 

17 

10 

17 

16 

16 

26 

26 

26 

29 

30 

27 

19 

12 

8 

10 

16 

21 

19 

17 

19 

87 

25 

87 

30 

31 

27 

19 

13 

10 

13 

1!) 

83 

99 

19 

18 

21 

98 

25 

28 

32 

97 

20 

14 

13 

17 

89 

25 

83 

20 

lil 

94 

89 

26 

30 

34 

33 

28 

20 

16 

15 

20 

25 

26 

23 

20 

20 

86 

an 

28 

32 

36 

34 

28 

21 

17 

18 

23 

27 

27 

23 

80 

21 

27 

31 

30 

35 

38 

35 

28 

21 

19 

20 

86 

28 

27 

89 

19 

21 

28 

32 

33 

38 

39 

85 

28 

22 

.20 

23 

97 

28 

26 

21 

18 

21 

29 

33 

35 

40 

40 

36 

27 

22 

21 

24 

28 

28 

24 

19 

17 

21 

29 

34 

33 

42 

41 

35 

27 

22 

22 

25 

28 

27 

22 

17 

16 

21 

89 

35 

40 

44 

41 

34 

26 

21 

22 

25 

27 

25 

19 

14 

IB 

81 

29 

36 

43 

45 

41 

33 

86 

21 

99 

25 

25 

22 

16 

12 

14 

21 

29 

37 

4.-, 

45 

40 

31 

2:! 

20 

22 

24 

23 

19 

13 

10 

13 

21 

80 

38 

46 

46 

38 

28 

21 

19 

21 

22 

90 

16 

9 

8 

13 

21 

',':> 

39 

46 

43 

36 

25 

19 

18 

19 

20 

17 

11 

6 

7 

14 

89 

29 

40 

46 

41 

32 

99 

17 

16 

17 

18 

14 

8 

4 

6 

14 

23 

29 

41 

4.') 

38 

9t) 

19 

14 

14 

15 

15 

10 

5 

3 

6 

in 

24 

30 

42 

44 

39 

24 

15 

19 

19 

14 

12 

7 

2 

2 

7 

17 

26 

31 

43 

41 

31 

90 

19 

10 

10 

19 

9 

5 

1 

2 

B 

90 

28 

33 

44 

38 

27 

16 

B 

8 

9 

10 

7 

3 

0 

3 

12 

23 

31 

86 

45 

34 

23 

12 

6 

(i 

9 

9 

6 

2 

0 

5 

16 

27 

36 

37 

46 

30 

18 

!l 

4 

5 

8 

8 

5 

2 

2 

9 

21 

M 

39 

40 

47 

26 

14 

6 

3 

5 

8 

8 

5 

3 

5 

14 

27 

37 

43 

43 

48 

89 

11 

4 

3 

6 

8 

8 

5 

5 

8 

20 

33 

42 

47 

47 

49 

18 

8 

3 

3 

7 

9 

9 

7 

8 

14 

27 

39 

48 

51 

51 

50 

15 

5 

2 

4 

9 

12 

11 

10 

13 

21 

34 

46 

54 

56 

55 

51 

12 

4 

3 

6 

19 

15 

14 

14 

18 

28 

42 

53 

60 

60 

ED 

E9I 

10 

4 

5 

10 

IB 

18 

18 

19 

85 

36 

50 

60 

65 

64 

62 

53 

9 

B 

7 

14 

1!) 

89 

23 

96 

33 

44 

58 

67 

70 

68 

66 

54 

8 

7 

11 

19 

24 

27 

28 

32 

41 

53 

66 

73 

74 

71 

li'.i 

55 

n 

10 

16 

24 

29 

32 

34 

39 

49 

62 

73 

78 

77 

74 

79 

56 

11 

14 

22 

30 

35 

38 

40 

46 

:.7 

70 

80 

83 

80 

76 

74 

57 

14 

]!> 

28 

36 

41 

43 

47 

63 

6B 

77 

86 

86 

82 

77 

75 

58 

17 

24 

35 

43 

47 

49 

53 

61 

73 

84 

90 

88 

-.1 

77 

7."> 

69 

22 

30 

42 

4!) 

69 

.-,:, 

59 

68 

80 

89 

09 

89 

82 

76 

75 

60 

27 

37 

48 

55 

58 

60 

86 

78 

85 

93 

94 

88 

rtl 

75 

71 

\\li.Tt  224-" .7  is  nulitractccl  from  Arg.  I.,  add  33.26  to  Arg.  X. 


TABL.E   XXXIII. 


Perturbations  of  Log.  r,  by  l/ic  Earth. 

Horizontal  Argument  =  I. 

Constant  added  15(1.           Period  of  Argument  I.,  224''.7. 

Arg. 
XI. 

d 

o 

d 
8 

A 

16 

d 

M 

d 

32 

d 

40 

d 

48 

d 

50 

d 

64 

d 

72 

d 

8O 

d 

88 

d 

96 

d 

1O4 

d 

112 

0 

206 

207 

211 

216 

220 

224 

225 

223 

219 

214 

809 

204 

202 

202 

205 

2 

210 

210 

213 

217 

222 

225 

887 

226 

>>•>•> 

218 

212 

207 

204 

202 

204 

4 

213 

213 

214 

218 

221 

224 

226 

225 

822 

217 

212 

206 

202 

200 

200 

6 

216 

214 

214 

217 

219 

222 

223 

222 

218 

214 

209 

203 

198 

195 

194 

8 

214 

212 

212 

214 

216 

218 

219 

218 

215 

210 

205 

198 

193 

190 

188 

in 

209 

207 

207 

209 

211 

213 

214 

214 

211 

207 

201 

195 

190 

185 

184 

12 

199 

196 

197 

200 

203 

206 

209 

210 

208 

205 

200 

194 

188 

183 

181 

14 

184 

182 

183 

187 

192 

197 

202 

204 

204 

202 

199 

193 

189 

184 

180 

Hi 

167 

1G6 

i<;~ 

172 

178 

1  rC> 

192 

196 

199 

198 

197 

193 

188 

183 

180 

18 

151 

150 

151 

156 

162 

170 

179 

185 

189 

191 

191 

188 

184 

181 

178 

90 

140 

137 

137 

141 

147 

165 

164 

171 

176 

180 

180 

179 

176 

173 

171 

22 

i:i:i 

129 

127 

130 

134 

141 

14!> 

156 

161 

165 

167 

165 

163 

160 

159 

24 

130 

126 

123 

123 

126 

131 

137 

143 

147 

150 

153 

150 

148 

145 

144 

26 

139 

125 

121 

131 

122 

126 

130 

134 

137 

139 

139 

136 

133 

129 

127 

28 

127 

125 

123 

I'" 

183 

125 

128 

131 

133 

134 

132 

128 

123 

118 

114 

30 

121 

122 

122 

123 

125 

128 

131 

134 

135 

135 

133 

128 

120 

113 

106 

32 

109 

114 

118 

189 

126 

131 

136 

140 

142 

143 

140 

134 

126 

115 

105 

34 

92 

101 

108 

116 

124 

132 

140 

146 

151 

153 

152 

146 

137 

125 

112 

36 

74 

84 

95 

1(16 

117 

128 

140 

150 

157 

162 

163 

159 

150 

138 

123 

38 

55 

66 

79 

92 

106 

120 

134 

147 

158 

167 

170 

169 

162 

150 

136 

40 

41 

51 

62 

76 

90 

106 

123 

138 

152 

164 

171 

172 

169 

160 

147 

42 

33 

39 

48 

60 

74 

90 

107 

124 

140 

IK 

165 

170 

170 

164 

154 

44 

31 

33 

38 

47 

58 

72 

89 

107 

124 

140 

153 

162 

166 

164 

157 

46 

36 

32 

33 

37 

45 

56 

72 

88 

106 

124 

138 

150 

158 

160 

156 

48 

45 

36 

32 

31 

35 

44 

56 

71 

8!) 

107 

124 

138 

148 

153 

153 

r>o 

58 

45 

35 

30 

30 

35 

44 

57 

73 

91 

109 

125 

137 

145 

149 

r>2 

75 

58 

44 

35 

29 

30 

36 

47 

61 

77 

95 

111 

126 

1  35 

142 

54 

90 

76 

58 

44 

34 

31 

32 

39 

50 

65 

81 

98 

113 

124 

132 

56 

121 

100 

79 

61 

46 

36 

33 

34 

42 

53 

68 

83 

98 

110 

120 

58 

150 

128 

106 

83 

64 

49 

39 

35 

37 

44 

55 

68 

81 

94 

104 

60 

181 

160 

137 

112 

89 

69 

53 

42 

38 

39 

46 

55 

66 

77 

87 

62 

211 

193 

171 

145 

120 

95 

74 

58 

47 

42 

43 

47 

55 

64 

72 

64 

236 

223 

203 

180 

154 

127 

102 

82 

65 

54 

49 

48 

51 

57 

63 

66 

253 

245 

231 

212 

188 

163 

136 

113 

93 

77 

67 

61 

59 

60 

63 

68 

261 

259 

251 

238 

219 

197 

173 

149 

127 

109 

94 

84 

78 

75 

73 

70 

259 

263 

263 

256 

244 

228 

207 

186 

165 

146 

129 

116 

106 

100 

94 

72 

251 

260 

265 

265 

261 

251 

236 

219 

201 

183 

166 

152 

141 

131 

122 

74 

241 

252 

261 

267 

269 

265 

257 

245 

231 

216 

201 

187 

175 

164 

154 

76 

233 

244 

254 

263 

269 

271 

268 

262 

253 

242 

23!  1 

217 

206 

196 

186 

78 

228 

237 

247 

257 

264 

270 

271 

270 

265 

258 

249 

240 

231 

223 

214 

80 

228 

233 

241 

249 

257 

264 

268 

270 

270 

266 

261 

255 

250 

243 

237 

82 

231 

232 

236 

242 

249 

2r,6 

262 

267 

269 

26!) 

268 

265 

262 

259 

255 

84 

236 

233 

233 

237 

242 

248 

254 

261 

265 

268 

270 

271 

271 

270 

269 

86 

236 

232 

231 

232 

,234 

240 

246 

253 

259 

265 

270 

273 

276 

278 

279 

88 

235 

230 

227 

226 

227 

231 

237 

244 

252 

260 

267 

273 

279 

283 

287 

90 

229 

225 

221 

219 

219 

222 

226 

233 

242 

251 

260 

269 

277 

284 

290 

02 

220 

218 

214 

211 

209 

210 

214 

220 

228 

237 

248 

259 

269 

278 

286 

94 

210 

209 

206 

203 

199 

198 

19!l 

203 

210 

218 

229 

241 

253 

265 

276 

96 

198 

199 

197 

194 

189 

185 

184 

is:, 

189 

195 

205 

217 

229 

243 

257 

98 

183 

188 

188 

184 

179 

173 

169 

166 

167 

170 

178 

188 

201 

216 

231 

100 

167 

174 

176 

174 

169 

162 

155 

150 

147 

147 

152 

159 

171 

185 

202 

102 

147 

156 

161 

162 

158 

151 

143 

136 

130 

127 

129 

133 

142 

155 

171 

104 

122 

135 

143 

146 

145 

140 

133 

126 

118 

113 

111 

112 

118 

128 

143 

106 

95 

no 

121 

128 

130 

128 

123 

117 

109 

103 

98 

97 

99 

106 

118 

108 

68 

84 

97 

106 

112 

114 

112 

107 

101 

94 

88 

85 

85 

89 

97 

110 

45 

60 

73 

84 

92 

.  97 

98 

96 

92 

86 

80 

75 

73 

74 

79 

112 

28 

40 

52 

63 

72 

79 

83 

83 

80 

76 

70 

65 

61 

63 

62 

114 

21 

29 

37 

46 

54 

61 

65 

67 

66 

64 

59 

53 

49 

46 

46 

116 

23 

26 

30 

36 

41 

46 

50 

52 

52 

51 

47 

42 

37 

33 

31 

118 

32 

30 

31 

32 

34 

37 

39 

41 

41 

39 

36 

32 

27 

22 

1!) 

ISO 

45 

41 

38 

35 

33 

33 

33 

34 

34 

33 

30 

27 

22 

17 

12 

1 

The  perturbations  are  in  units  of  the  eighth  decimal  place.. 


TABLE   XXXIII. 


1'i'rliirtiti/iiiiia  of  Lin;.  /-,  tit/  llir  i'.iirlli. 

llun/tint;;!  Argument  =  I. 

("iui>l;ml  lidded  I.Mi.        r.Timl  i>f  Argument  XI.,  210  units. 

d 

.1 

,, 

d 

.1 

d 

,1 

d 

d 

d 

d 

d 

d 

d 

Arg  XI 

120 

12* 

136 

111 

142 

160 

16N 

ire 

184 

192 

200 

20N 

216 

»»• 

*»2 

0 

310 

217 

224 

931 

935 

939 

2:58 

937 

236 

936 

939 

-Ml 

959 

21,2 

3 

•JiT 

919 

918 

923 

237 

•.'-'.i 

997 

326 

997 

930 

936 

945 

956 

4 

909 

906 

211 

915 

918 

22',  i 

221    219 

•-'17 

316 

916 

910 

995 

934 

2H> 

6 

106 

199 

•Jl)-' 

•J  '. 

910 

•-'ID 

•Jill 

906 

911 

990 

939 

8 

189 

11)1 

194 

107 

199 

199 

199 

100 

193 

1:1.1 

188 

10(1 

194 

203 

916 

10 

is:! 

l-l 

l-i, 

188 

189 

188 

186 

183 

178 

171 

171 

171 

173 

181 

193 

19 

170 

180 

l-  i 

l-l 

1-  i 

178 

171 

169 

169 

156 

150 

1  1- 

1  l:> 

[56 

166 

1  1 

17- 

177 

I7(> 

176 

174 

170 

Mil 

156 

1  17 

138 

130 

125 

194 

[98 

138 

Hi 

177 

176 

17.') 

173 

170 

!  (  ).') 

167 

148 

136 

194 

113 

106 

III! 

109 

100 

IS 

17.') 

171 

173 

172 

169 

164 

166 

145 

131 

117 

102 

01 

83 

81 

-1 

30 

170 

169 

170 

170 

His 

164 

158 

117 

134 

118 

101 

87 

75 

68 

67 

99 

ISO 

160 

163 

165 

167 

166 

H,  -J 

153 

1  I-J 

196 

109 

99 

76 

(i"i 

60 

•-'1 

1  II 

147 

151 

157 

162 

165 

166 

161 

1  .-,-' 

139 

122 

105 

87 

7-.' 

62 

36 

I'Js 

130 

136 

144 

153 

160 

1  65 

165 

161 

151 

137 

I-JI 

103 

B6 

73 

98 

113 

114 

190 

198 

138 

1  1  • 

168 

163 

164 

160 

150 

137 

120 

103 

88 

30 

109 

loo 

104 

111 

121 

133 

145 

,.-,, 

H,i 

161 

156 

147 

184 

119 

111) 

'.is 

09 

01 

06 

104 

115 

[98 

139 

149 

154 

156 

I.MI 

149 

130 

118 

34 

Hill 

n  i 

85 

84 

89 

98 

100 

199 

133 

149 

147 

147 

143 

136 

198 

36 

lu- 

95 

79 

79 

-1 

03 

104 

Hi, 

197 

135 

130 

140 

137 

I.!! 

ll!) 

103 

90 

80 

75 

76 

82 

01 

109 

114 

123 

130 

134 

135 

134 

•1  1 

131 

113 

98 

86 

78 

7.-, 

77 

84 

93 

1  •! 

III 

122 

128 

131 

133 

4-.' 

11) 

134 

108 

94 

84 

78 

78 

89 

89 

98 

107 

III, 

193 

127 

I'.'i  ) 

44 

146 

132 

117 

103 

02 

85 

82 

84 

89 

96 

104 

119 

118 

193 

1J7 

46 

1  in 

137 

I'.'l 

111 

Hill 

99 

88 

87 

90 

95 

109 

108 

114 

119 

122 

48 

149 

141 

[99 

118 

HI7 

99 

93 

91 

92 

95 

100 

105 

HO 

113 

116 

50 

147 

141 

133 

123 

113 

104 

98 

94 

94 

05 

98 

101 

105 

107 

100 

59 

143 

140 

133 

135 

116 

KM 

101 

97 

06 

96 

96 

101 

109 

103 

54 

136 

135 

131 

195 

117 

111 

105 

100 

98 

98 

98 

99 

100 

09 

137 

125 

122 

117 

112 

108 

105 

103 

103 

103 

103 

102 

101 

99 

58 

119 

116 

116 

116 

113 

HI 

110 

109 

109 

110 

111 

111 

111 

108 

HIl 

60 

96 

101 

105 

107 

108 

108 

110 

112 

115 

118 

121 

123 

123 

120 

115 

62 

81 

87 

02 

96 

99 

102 

107 

112 

II!) 

I-J.-, 

131 

135 

136 

135 

139 

64 

70 

75 

80 

84 

89 

94 

100 

108 

117 

127 

136 

144 

148 

149 

146 

66 

66 

70 

73 

76 

70 

84 

91 

100 

111 

123 

135 

146 

155 

I.V.I 

i  .,- 

68 

73 

72 

72 

73 

74 

76 

81 

98 

100 

114 

129 

142 

[55 

163 

166 

70 

89 

85 

81 

77 

74 

73 

75 

81 

90 

103 

118 

133 

148 

161 

H,- 

72 

114 

107 

99 

91 

84 

78 

76 

77 

83 

93 

107 

123 

140 

155 

11,1, 

74 

144 

134 

193 

112 

101 

99 

84 

82 

83 

90 

101 

115 

132 

148 

162 

76 

176 

16.1 

153 

140 

126 

114 

103 

96 

03 

95 

ID--' 

114 

128 

144 

I.V.I 

78 

205 

195 

183 

170 

156 

142 

129 

118 

111 

109 

112 

J20 

131 

146 

169 

/SO 

230 

232 

212 

200 

187 

172 

158 

145 

136 

130 

no 

133 

141 

l.-.l 

169 

82 

250 

244 

237 

•J->7 

215 

202 

1  — 

174 

163 

154 

150 

150 

155 

161 

171) 

84 

366 

263 

958 

950 

240 

228 

214 

200 

188 

178 

171 

168 

169 

173 

179 

86 

279 

278 

274 

268 

260 

24!) 

236 

222 

208 

107 

189 

l-l 

183 

l-l 

180 

88 

289 

288 

287 

282 

274 

264 

252 

238 

225 

212 

909 

196 

193 

194 

197 

90 

293 

295 

295 

291 

285 

275 

263 

250 

236 

224 

213 

205 

201 

200 

203 

02 

293 

297 

298 

296 

291 

283 

272 

259 

945 

232 

•91 

212 

2.16 

905 

94 

285 

292 

2!Ki 

297 

204 

287 

277 

265 

252 

23!  » 

227 

218 

919 

909 

210 

96 

269 

279 

288 

291 

291 

2  —  : 

280 

270 

258 

MS 

233 

223 

916 

213 

919 

98 

246 

260 

272 

280 

284 

283 

279 

271 

261 

949 

237 

228 

220 

215 

313 

100 

219 

236 

251 

262 

270 

273 

272 

267 

259 

248 

238 

228 

220 

916 

919 

1  AO 

189 

207 

240 

251 

258 

959 

257 

251 

949 

933 

224 

2  Hi 

210 

•-'  '7 

m 
104 
106 

108 

160 
133 
109 

178 
150 
125 

197 
169 
142 

214 
186 

159 

227 
201 
174 

237 
913 

1-7 

241 
219 
196 

2  12 
222 

-Jin 

938 

3:>o 

231 
214 

196 

999 

207 
189 

214 

199 
182 

206 
192 
175 

201 
1-7 
170 

10.1 
185 

MO 

110 
112 
114 
116 
118 
120 

83 

50 
32 

18 
10 

101 

79 
58 
39 
22 
11 

116 
99 

7.) 
4!) 
30 
16 

133 

-1 
62 
42 
24 

149 
121 
101 

78 
57 
37 

162 
139 
117 
96 

71 
53 

173 
151 

131 
112 
92 
71 

179 
169 
142 
195 

107 

87 

i-  > 

16  1 
149 

135 
121 
103 

17s 
Hi:: 
151 
140 

199 
116 

173 
150 
150 
149 
135 
194 

166 
153 
146 

140 

136 

128 

150 

117 
1:1:1 
135 
133 
199 

166 

142 

134 
130 
199 
127 

153 
139 
130 
196 
193 
183 

\Vlicn  2-,M''.7  is  subtracted  from  Arg.  1.,  add  147.61  to  Arg.  XI. 

TABLE  XXXIII. 


Perturbations  of  Log.  ?-,  l>y  the  Earth. 

Horizontal  Argument  =  I. 

Constant  added  150.           Period  of  Argument  1.,  224<i.7. 

d 

d        d 

d 

d 

d 

d 

d 

d 

d 

d 

.  d 

d 

d 

d 

Arg.X 

0 

i 

16 

24 

32 

40 

48 

56 

64 

72 

sa 

<*8 

96 

1O4 

112 

120 

45 

41 

38 

35 

33 

33 

.3» 

34 

34 

33 

30 

27 

22 

17 

12 

129 

60 

54 

48 

43 

38 

36 

34 

33 

33 

32 

30 

23 

23 

18 

13 

124 

74 

68 

61 

55 

48 

44 

40 

33 

33 

37 

36 

35 

31 

26 

20 

126 

88 

82 

76 

68 

61 

55 

50 

47 

46 

45 

46 

46 

44 

40 

34 

123 

102 

98 

91 

83 

75 

63 

62 

58 

56 

55 

56 

58 

57 

55 

51 

130 

118 

114 

108 

100 

92 

83 

76 

69 

66 

65 

66 

63 

69 

69 

68 

139 

138 

135 

129 

120 

111 

100 

90 

82 

76 

73 

73 

75 

78 

8.) 

81 

134 

162 

158 

152 

144 

133 

120 

107 

96 

87 

81 

79 

80 

83 

87 

91 

136 

187 

184 

178 

16!) 

158 

144 

123 

114 

101 

91 

86 

84 

86 

91 

97 

138 

211 

209 

805 

197 

185 

170 

153 

136 

120 

106 

97 

92 

92 

95 

101 

MO 

232 

232 

22!) 

983 

213 

1!)!) 

\-> 

164 

145 

128 

115 

106 

102 

103 

108 

142 

847 

24!) 

251 

247 

240 

22!) 

213 

195 

175 

157 

13!) 

127 

11!) 

116 

117 

144 

255 

260 

264 

963 

263 

255 

213 

227 

218 

188 

16!) 

153 

141 

134 

131 

146 

256 

264 

271 

277 

27!) 

277 

268 

256 

240 

221 

2i)l 

132 

167 

156 

149 

14H 

252 

262 

273 

282 

288 

2!)] 

288 

279 

266 

350 

230 

211 

193 

179 

163 

ir,n 

244 

256 

268 

281 

291 

297 

299 

295 

286 

272 

255 

237 

218 

201 

187 

152 

233 

245 

35'J 

273 

286 

297 

302 

3D3 

298 

233 

274 

257 

239 

222 

2.16 

1  54 

21!) 

231 

246 

261 

276 

239 

2!)3 

303 

303 

297 

236 

272 

255 

239 

222 

156 

201 

213 

228 

244 

261 

276 

23!) 

21)8 

301 

300 

293 

283 

26!) 

254 

•j:!3 

158 

178 

too 

205 

222 

240 

25!) 

275 

237 

295 

298 

296 

290 

230 

267 

253 

16!) 

152 

163 

173 

E96 

216 

236 

255 

272 

284 

292 

296 

294 

233 

27!) 

267 

162 

124 

133 

148 

166 

187 

210 

232 

252 

269 

231 

289 

993 

292 

287 

27!) 

Ki4 

D8 

1(15 

118 

135 

156 

ISO 

204 

227 

217 

263 

276 

235 

289 

289 

286 

166 

77 

81 

91 

106 

125 

148 

173 

197 

219 

239 

256 

26!) 

277 

989 

984 

HH 

66 

65 

70 

81 

98 

118 

141 

164 

183 

208 

227 

243 

256 

265 

272 

170 

65 

59 

59 

65 

77 

93 

112 

133 

154 

174 

193 

211 

225 

238 

250 

172 

74 

63 

58 

58 

64 

75 

89 

106 

124 

141 

tss 

175 

190 

204 

219 

174 

88 

75 

65 

61 

61 

66 

75 

87 

100 

114 

127 

141 

155 

16!) 

184 

176 

105 

90 

78 

71 

67 

63 

71 

78 

87 

96 

105 

114 

125 

136 

14!) 

178 

120 

1C6 

94 

85 

79 

77 

77 

80 

84 

89 

93 

98 

104 

111 

120 

180 

131 

120 

109 

100 

94 

90 

89 

90 

91 

92 

92 

93 

93 

94 

98 

182 

136 

123 

120 

114 

109 

106 

104 

104 

103 

102 

100 

96 

92 

88 

86 

184 

137 

133 

128 

124 

121 

119 

11!) 

119 

118 

116 

112 

105 

97 

88 

81 

186 

135 

134 

132 

131 

129 

12!) 

130 

130 

131 

129 

124 

116 

106 

94 

81 

m 

131 

133 

133 

133 

134 

135 

137 

138 

139 

138 

134 

126 

114 

101 

85 

100 

127 

S30 

132 

133 

135 

137 

139 

142 

144 

143 

140 

133 

122 

108 

91 

199 

123 

126 

129 

131 

133 

135 

138 

142 

145 

146 

144 

13!) 

129 

115 

98 

1!)4 

118 

122 

124 

126 

129 

131 

135 

140 

144 

147 

147 

143 

135 

122 

106 

196 

113 

115 

118 

12:) 

123 

126 

131 

136 

142 

146 

148 

147 

141 

130 

115 

196 

106 

108 

1JO 

112 

115 

119 

124 

131 

138 

144 

149 

150 

147 

139 

126 

200 

101 

102 

103 

104 

106 

111 

117 

124 

133 

141 

147 

152 

151 

146 

136 

202 

i)8 

98 

97 

97 

!)!) 

102 

108 

115 

124 

134 

1  12 

149 

152 

150 

142 

204 

102 

99 

96 

94 

93 

94 

!)3 

104 

113 

123 

133 

142 

147 

148 

144 

206 

11)9 

105 

1  00 

95 

91 

8!) 

90 

94 

101 

111 

120 

130 

138 

142 

141 

208 

122 

117 

no 

102 

95 

89 

86 

86 

91 

98 

107 

117 

125 

132 

134 

210 

137 

132 

124 

114 

104 

94 

87 

84 

84 

89 

96 

105 

114 

121 

125 

919 

151 

148 

140 

130 

118 

106 

95 

88 

85 

86 

90 

93 

106 

113 

11!) 

214 

161) 

160 

155 

146 

134 

121 

109 

99 

93 

92 

93 

98 

105 

112 

118 

216 

163 

167 

166 

160 

150 

138 

126 

116 

108 

104 

104 

107 

112 

118 

123 

218 

160 

169 

171 

170 

164 

154 

144 

134 

126 

121 

120 

122 

126 

131 

135 

220 

154 

166 

173 

176 

173 

167 

159 

151 

144 

139 

137 

139 

143 

147 

152 

222 

148 

162 

172 

173 

17!) 

176 

171 

164 

153 

154 

153 

154 

153 

164 

168 

224 

145 

159 

171 

173 

182 

181 

178 

173 

168 

164 

164 

166 

170 

177 

183 

226 

147 

160 

171 

17!) 

184 

184 

182 

177 

173 

170 

169 

172 

177 

185 

193 

228 

154 

165 

175 

182 

187 

137 

185 

181 

177 

173 

172 

174 

180 

188 

198 

230 

164 

173 

181 

137 

191 

192 

189 

185 

180 

175 

174 

175 

180 

189 

2!)0 

232 

176 

182 

189 

194 

198 

198 

194 

191 

185 

180 

177 

178 

182 

189 

aw 

234 

186 

191 

196 

201 

205 

805 

203 

199 

193 

188 

184 

183 

185 

191 

200 

236 

195 

198 

203 

203 

212 

213 

212 

2!)8 

2)3 

197 

193 

190 

190 

194 

809 

238 

eoi 

204 

2:  is 

213 

217 

22;) 

22D 

217 

212 

207 

202 

198 

197 

199 

2.)4 

240 

206 

207 

211 

216 

220 

224 

225 

223 

21!) 

214 

21)!) 

204 

202 

202 

205 

The  perturbations  are  in  units  of  the  eighth  decimal  pla.cc. 


TABLE   XXXIII. 


I'l-rliir/iii/iniix  nf  /.n:,'.  r,  lij  tin-  I-'.arlh. 

II      i  \  _•  .iini'iii  =  1. 

('"ii-t.-int  inlili-il  150        IVrhid  oi'Ar^ii  nt  XI.,  ','10  unit*. 

Arg.X 

a 
1  20 

.1 
12* 

.1 

i::<; 

,i 
191 

.1 
152 

.1 
160 

!<;•» 

d 

17« 

111 

l<»v> 

200 

20W 

i 
210 

.1 
221 

,\ 
232 

190 

10 

II 

n> 

94 

37 

71 

-7 

ID: 

ue 

194 

r.'- 

I3H 

127 

196 

199 

- 

6 

6 

12 

91 

34 

•1! 

66 

8* 

06 

IH- 

116 

191 

122 

199 

194 

II 

0 

6 

6 

ID 

19 

31 

11 

71 

-7 

97 

100 

111 

115 

!•.'(> 

27 

90 

i:< 

9 

8 

11 

17 

86 

51 

64 

76 

86 

06 

11)3 

hid 

II 

87 

•J- 

21) 

14 

11 

11 

10 

93 

39 

43 

54 

66 

71, 

86 

130 

63 

66 

47 

37 

28 

21 

16 

IB 

iii 

21 

86 

36 

47 

57 

69 

139 

80 

7(i 

69 

60 

4!) 

40 

31 

•-.':> 

21 

90 

88 

37 

34 

42 

52 

134 

09 

D9 

33 

71 

64 

63 

44 

36 

39 

87 

26 

86 

33 

40 

136 

109 

105 

i  6 

104 

96 

DO 

7!) 

69 

58 

1- 

40 

34 

31 

30 

33 

138 

109 

115 

190 

191 

110 

114 

106 

96 

83 

71 

49 

40 

35 

38 

140 

tie 

193 

130 

13:> 

137 

|36 

199 

121 

109 

06 

81 

67 

54 

44 

35 

149 

193 

130 

139 

145 

ISO 

159 

14!) 

149 

139 

119 

IDI 

87 

71 

56 

44 

1  II 

139 

139 

146 

154 

hi) 

164 

161 

161 

153 

141 

196 

111!) 

Dl 

73 

67 

i  ni 

147 

14!) 

164 

Hi:) 

167 

17:1    176 

17.-. 

171 

nil 

II- 

132 

113 

!H 

75 

148 

162 

100 

162 

167 

174 

1-  i 

186 

188 

187 

181 

171 

156 

ISO 

II- 

97 

160 

17- 

173 

172 

174 

180 

187 

194 

1!'!) 

801 

190 

193 

182 

166 

147 

196 

IS9 

193 

l-:, 

181 

189 

186 

199 

200 

208 

213 

915 

914 

906 

I9S 

178 

157 

154 

208 

196 

101 

189 

199 

197 

2Dr> 

213 

888 

998 

831 

228 

221 

207 

189 

166 

894 

212 

202 

tee 

197 

200 

207 

216 

996 

935 

241 

244 

849 

233 

219 

158 

239 

226 

916 

207 

204 

204 

208 

916 

224 

2:15 

-'II 

251 

854 

251 

843 

tfiO 

968 

242 

229 

21!) 

212 

90fj 

208 

212 

'Jill 

229 

240 

250 

958 

260 

867 

169 

96U 

957 

^'11 

2!!2 

888 

214 

210 

210 

314 

221 

931 

841 

253 

850 

863 

164 

979 

969 

258 

246 

934 

983 

915 

911 

•.'in 

•_'l  1 

881 

930 

94S 

858 

261 

166 

989 

976 

969 

-.'17 

225 

217 

911 

211 

214 

991 

231 

949 

833 

103 

973 

27.-, 

271! 

267 

356 

248 

837 

228 

819 

914 

213 

216 

884 

233 

811 

170 

258 

964 

268 

268 

265 

258 

350 

•.'  1  1 

232 

n  i 

220 

218 

222 

889 

237 

17'.' 

232 

943 

963 

960 

963 

963 

260 

254 

246 

231 

896 

885 

896 

833 

174 

199 

•JI4 

930 

242 

953 

930 

969 

261 

257 

850 

243 

236 

2:12 

830 

232 

176 

164 

l-l 

1!)!) 

216 

939 

845 

954 

260 

257 

252 

245 

830 

935 

232 

178 

189 

147 

165 

184 

•.'  >  1 

929 

236 

248 

954 

8.V, 

253 

248 

818 

837 

833 

180 

106 

117 

132 

150 

171 

I!M 

210 

226 

238 

245 

247 

245 

241 

236 

231 

t«9 

87 

99 

103 

117 

136 

157 

178 

19S 

914 

896 

233 

£16 

934 

831 

227 

l-l 

76 

75 

79 

89 

105 

193 

144 

166 

186 

21)2 

814 

221 

883 

983 

890 

146 

71 

64 

63 

67 

78 

:>:t 

113 

135 

156 

176 

192 

203 

909 

212 

211 

188 

71 

6!) 

52 

51 

57 

68 

85 

106 

128 

150 

16!! 

184 

1!I4 

200 

201 

190 

74 

Be 

47 

41 

42 

49 

63 

81 

102 

124 

11.-, 

161 

177 

186 

190 

199 

80 

62 

47 

37 

33 

35 

44 

59 

78 

100 

199 

142 

158 

I6B 

176 

194 

88 

69 

61 

37 

28 

26 

2!) 

40 

r,7 

76 

B7 

118 

136 

II!) 

15!  t 

l:ni 

W 

78 

58 

41 

28 

21 

20 

85 

36 

58 

71 

!)l 

110 

196 

ISO 

l!H 

109 

88 

69 

49 

32 

20 

14 

14 

20 

:'.! 

47 

65 

83 

M 

114 

200 

121 

101 

81 

60 

40 

85 

13 

H 

9 

15 

26 

40 

56 

7'.' 

87 

909 

130 

113 

94 

73 

r>8 

34 

19 

9 

4 

5 

11 

21 

34 

48 

63 

904 

135 

199 

105 

86 

65 

46 

30 

17 

9 

5 

6 

11 

19 

80 

42 

906 

136 

126 

113 

97 

7!) 

61 

44 

31 

80 

13 

10 

11 

14 

21 

29 

208 

133 

127 

118 

105 

91 

76 

61 

48 

37 

23 

83 

20 

19 

21 

25 

210 

127 

196 

119 

.110 

100 

88 

76 

(»-, 

.-,.-, 

46 

40 

35 

31 

30 

29 

212 

122 

139 

190 

114 

106 

98 

88 

80 

72 

64 

58 

63 

47 

43 

38 

914 

121 

193 

191 

117 

111 

105 

!I7 

01 

96 

79 

74 

69 

63 

58 

58 

916 

127 

I9t! 

197 

122 

117 

111 

104 

BO 

05 

90 

87 

83 

78 

72 

<;o 

218 

138 

IJO 

136 

132 

126 

119 

113 

107 

103 

100 

97 

M 

M 

86 

80 

220 

154 

l.->4 

152 

147 

139 

132 

124 

118 

113 

no 

107 

106 

103 

100 

06 

ygjll 

172 

I7:i 

170 

165 

158 

149 

140 

133 

127 

123 

121 

190 

118 

116 

119 

994 

188 

I!IO 

KM) 

186 

17!) 

171 

161 

163 

147 

142 

130 

138 

136 

136 

131 

996 

800 

205 

207 

206 

201 

194 

l-i, 

177 

170 

165 

161 

M,i 

160 

157 

I.M 

998 

21)7 

216 

221 

993 

221 

216 

209 

202 

l!Ki 

190 

186 

185 

184 

182 

17!l 

230 

211 

222 

230 

9M 

236 

234 

230 

224 

218 

213 

210 

209 

208 

207 

gD6 

232 

Iil2 

224 

234 

949 

246 

246 

944 

240 

2:16 

232 

890 

838 

889 

889 

8H 

831 

212 

883 

2:15 

243 

940 

951 

951 

249 

2  15 

949 

941 

241 

243 

846 

•-'17 

936 

211 

222 

939 

941 

217 

951 

•-•:>  1 

350 

•-'17 

946 

345 

946 

349 

884 

•-'.-,•1 

938 

•Jll 

00 

22!> 

•J37 

949 

•-M<; 

247 

246 

'.'11 

943 

949 

945 

340 

85f  i 

864 

940 

210 

217 

994 

231 

939 

2:t8 

239 

238 

937 

236 

236 

8*4 

252 

869 

13V 


When  224'' .7  is  subtracted  from  Arg.  I.,  add  147.61  to  Arg.  XI. 


410 


TABLE  XXXI V. 


Perturbations  nf  Log.  r,  by  Mars. 

Horizontal  Argument  =  I. 

.Constant  added  80.            Period  of  Argument  I.,  224<i.7. 

d 

A 

d 

d 

d 

1 

d 

d 

d 

d 

A 

d 

d 

d 

d 

Arg. 
XII. 

0 

8 

1C 

24 

32 

40 

48 

56 

6ft 

72 

80 

88 

96 

SOI 

112 

0 

!22 

106 

88 

71 

54 

38 

25 

15 

8 

g 

6 

11 

2; 

32 

46 

1 

!38 

124 

111! 

1)3 

76 

61) 

44 

30 

18 

1C 

7 

8 

11 

18 

29 

*> 

14<> 

140 

129 

115 

99 

82 

65 

49 

35 

24 

15 

10 

( 

11 

17 

3 

153 

14!) 

142 

132 

118    103 

87 

71 

r,r, 

40 

as 

1! 

14 

11 

12 

4 

150 

152 

150 

144 

134 

122 

108 

92 

76 

61 

46 

33 

24 

17 

13 

5 

140 

147 

150 

148 

143 

135 

125 

113 

97 

82 

67 

52 

39 

29 

21 

6 

125 

J36 

143 

147 

147 

114 

138 

128 

115 

102 

88 

73 

58 

45 

34 

7 

106 

120 

131 

140 

145 

146 

144 

139 

131 

121 

107 

93 

78 

64 

50 

8 

85 

101 

115 

126 

133 

142 

145 

144 

139 

132 

123 

112 

DO 

84 

71 

9 

64 

79 

94 

108 

120 

130 

138 

142 

143 

140 

134 

120 

116 

104 

91 

10 

45 

59 

73 

88 

102 

115 

126 

134 

139 

141 

140 

136 

129 

120 

109 

11 

30 

41 

54 

68 

82 

97 

110 

120 

129 

135 

139 

139 

137 

132 

1  24 

12 

19 

27 

37 

49 

61 

75 

DO 

103 

115 

1  25 

132 

137 

139 

137 

133 

13 

16 

1!) 

25 

33 

44 

56 

69 

83 

96 

108 

119 

J27 

133 

i:i~ 

137 

14 

18 

17 

18 

22 

30 

40 

51 

64 

77 

90 

102 

114 

123 

130 

135 

15 

28 

sa 

19 

19 

22 

27 

35 

45 

57 

70 

83 

96 

108 

118 

126 

16 

43 

:!:! 

26 

21 

19 

21 

25 

31 

40 

51 

63 

76 

89 

101 

112 

17 

:>:> 

47 

37 

29 

23 

20 

20 

23 

28 

36 

46 

58 

70 

84 

96 

18 

80 

07     54 

43 

33 

26 

21 

20 

21 

25 

31 

40 

51 

62 

75 

19 

101 

87 

74 

60 

48 

38 

30 

24 

21 

20 

22 

27 

35 

45 

56 

20 

II!) 

106 

92 

79 

66 

53 

43 

33 

26 

21 

19 

21) 

24 

31 

40 

21 

133 

iaa 

111 

99 

86 

73 

59 

47 

37 

29 

23 

19 

18 

2!) 

K 

22 

142 

136 

128 

118 

105 

92 

79 

65 

53 

42 

32 

24 

19 

17 

18 

23 

144 

143 

139 

132 

^'>•> 

111 

99 

86 

72 

58 

46 

35 

26 

20 

16 

24 

141 

144 

144 

141 

135 

127 

117 

105 

N 

78 

63 

51 

39 

29 

21 

25 

132 

139 

143 

144 

143 

138 

131 

122 

111 

98 

85 

70 

56 

43 

31 

26 

117 

127 

135 

141 

144 

144 

142 

136 

127 

117 

105 

91 

76 

61 

47 

27 

98 

111 

122 

132 

139 

143 

145 

143 

139 

132 

122 

110 

96 

82 

66 

28 

78 

93 

106 

118 

128 

137 

143 

146 

145 

142 

137 

128 

117 

103 

88 

2t) 

58 

71 

86 

99 

112 

124 

134 

142 

146 

147 

146 

141 

133 

122 

109 

30 

41 

52 

65 

79 

93 

107 

120 

130 

139 

145 

148 

148 

144 

137 

127 

31 

29 

37 

47 

60 

73 

88 

102 

115 

127 

137 

145 

149 

150 

148 

141 

32 

20 

24 

31 

42 

53 

67 

82 

96 

110 

123 

134 

144 

150 

152 

151 

33 

19 

18 

21 

26 

36 

47 

60 

75 

90 

105 

119 

131 

141 

149 

159 

34 

25 

20 

17 

18 

23 

32 

42 

55 

69 

85 

100 

115 

128 

139 

148 

35 

35 

27 

20 

16 

16 

20 

27 

37 

49 

63 

79 

95 

111 

125 

136 

36 

51 

39 

29 

21 

16 

15 

17 

23 

31 

43 

57 

73 

89 

105 

12U 

37 

69 

55 

43 

32 

22 

16 

13 

15 

19 

27 

38 

52 

67 

84 

100 

38 

90 

76 

61 

48 

34 

24 

16 

13 

12 

16 

23 

33 

46 

61 

78 

39 

110 

97 

82 

66 

51 

38 

27 

18 

13 

11 

13 

19 

29 

41 

56 

40 

128 

116 

102 

87 

72 

56 

42 

29 

19 

13 

10 

11 

16 

25 

36 

41 

140 

131 

121 

108 

93 

78 

61 

46 

32 

22 

14 

10 

10 

13 

21 

42 

148 

144 

137 

128 

114 

99 

83 

66 

50 

36 

24 

15 

10 

8 

11 

43 

148 

150 

148 

142 

132 

119 

105 

89 

71 

54 

39 

27 

17 

11 

8 

44 

141 

148 

150 

150 

145 

136 

124 

110 

94 

77 

59 

44 

31 

20 

12 

45 

130 

140 

148 

152 

152 

147 

140 

130 

116 

99 

82 

64 

49 

35 

23 

46 

112 

127 

138 

147 

153 

154 

151 

144 

133 

120 

104 

87 

69 

53 

38 

47 

90 

108 

123 

136 

146 

152 

155 

153 

147 

138 

125 

109 

92 

75 

58 

48 

68 

88 

104 

119 

133 

145 

152 

155 

154 

149 

141 

129 

114 

97 

81 

49 

46 

62 

81 

98 

115 

130 

142 

151 

156 

156 

152 

144 

133 

119 

103 

50 

27 

41 

57 

76 

93 

111 

127 

133 

149 

155 

156 

154 

147 

136 

123 

51 

13 

23 

36 

53 

70 

89 

107 

122 

136 

146 

154 

156 

155 

150 

140 

52 

3 

9 

19 

39 

48 

65 

84 

102 

118 

133 

144 

J52 

]5G 

156 

150 

53 

1 

2 

7 

15 

28 

44 

60 

79 

97 

114 

129 

141 

149 

154 

155 

54 

6 

2 

1 

4 

12 

24 

39 

55 

73 

92 

109 

125 

137 

146 

153 

55 

18 

9 

3 

1 

3 

10 

21 

35 

50 

68 

87 

104 

120 

133 

143 

56 

35 

21 

11 

4 

1 

3 

9 

18 

31 

46 

63 

82 

99 

115 

128 

57 

54 

39 

25 

14 

6 

2 

2 

i? 

16 

27 

42 

59 

76 

94 

110 

58 

79 

61 

44 

30 

18 

9 

4 

3 

6 

13 

24 

38 

54 

70 

87 

60 

102 

84 

67 

49 

33 

21 

12 

6 

4 

6 

12 

22 

35 

49 

65 

'  60 

122 

106 

88 

71 

54 

38 

25 

15 

8 

5 

6 

11 

20 

32 

46 

The  perturbations  arc  in  units  of  the  eighth  decimal  place. 


Tilt  Li:    XXXIV. 


Perturbations  «f  Lu<^.  /•,  A.-/  Mar*. 

rii>riz»iil;il                     i  =  1. 

('••n-liiut  ;icMi                                IVri"d  «,f  Argiiinrnl  XII.,  (ill  units. 

. 

j 

,j 

,i 

d 

.1 

.1 

d 

.1 

d 

xff 

120 

i:t«i 

111 

152 

100 

I«« 

l?« 

IM 

19» 

200 

20* 

210 

22  1 

2*2 

0 

1,1 

7,, 

09 

107 

121         131         i:i:> 

1  i:, 

11-          117 

149 

131 

195 

113 

100 

1 

49 

56 

71 

109 

III,          127 

136 

III 

li:, 

1  H, 

143 

137 

Itti 

118 

2 

96 

:',7 

51 

63 

8(1 

05 

109 

121 

131           13-           113 

li:, 

143 

IM 

133 

3 

17 

94 

31 

47 

GO 

71            -  i 

109 

115 

196 

136 

Ill 

111 

1  II 

149 

4 

12 

IS 

91 

31 

49 

:,:, 

89 

-•'• 

97 

llll 

191 

131 

138 

143 

144 

- 

16 

16 

16 

21 

99 

38 

r,ii 

a 

7i  ; 

103 

116 

196 

131 

140 

G 

95 

2  ' 

17 

17 

99 

96 

34 

IS 

",7 

69 

06 

no 

122 

131 

4 

38 

30 

23 

1!) 

18 

1!) 

21 

31 

41 

59 

(il 

77 

91 

106 

117 

8 

57 

4.-, 

3D 

27 

99 

•J  i 

90 

99 

9B 

36 

16 

."•7 

70 

84 

9 

7- 

Gl 

59 

II 

39 

96 

99 

90 

21 

95 

32 

40 

51 

G3 

7- 

ID 

06 

s:( 

7n 

57 

4G 

37 

23 

90 

20 

93 

3G            H, 

;,, 

11 

114 

109 

!NI 

78 

(>•"> 

63 

43 

31 

27 

99 

90 

21 

32 

41 

12 

127 

118 

108 

'.'7 

-1 

71 

50 

47 

37 

90 

93 

2,1            2  i 

99 

98 

13 

135 

130 

123 

II  1 

103 

90 

78 

65 

63 

42 

33 

21             1!) 

21 

14 

137 

136 

133 

127 

11!) 

108 

!I7 

85 

71 

58 

47 

37 

89 

1!) 

15 

139 

136 

137 

136 

130 

194 

116 

104 

99 

7- 

66 

53           41 

31 

23 

Hi 

199 

129 

135 

137 

136 

133 

198 

120 

no 

88 

85 

71 

58 

45 

31 

17 

108 

118 

196 

133 

137 

137 

13G 

132 

1  2~> 

115 

104 

91 

77 

63 

59 

18 

88 

101 

113 

193 

131 

137 

139 

138 

136 

130          122 

111             !H 

84 

60 

1!) 

6!) 

82 

90 

108 

120 

198 

136 

140 

141 

140 

135 

127 

117 

105 

1)1 

90 

51 

63 

76 

89 

103 

11.-, 

125 

134 

140 

112 

142 

138 

132 

122 

no 

34 

4.-, 

56 

69 

84 

111 

199 

139 

140 

III 

144 

142 

137 

198 

99 

99 

99 

38 

50 

G3 

77 

09 

106 

119 

CIO 

13!) 

144 

146 

145 

in 

98 

1G 

18 

24 

33 

44 

57 

71 

86 

101 

115 

127 

137 

144 

148 

149 

94 

16 

13 

14 

19 

27 

38 

51 

65 

81 

96 

111 

195 

136 

144 

14!) 

86 

99 

1G 

13 

13 

16 

23 

33 

44 

59 

7.'. 

91 

106 

121 

133 

143 

96 

34 

24 

16 

11 

10 

19 

18 

27 

39 

63 

G!) 

85 

109 

118 

131 

27 

59 

3!) 

27 

18 

12 

9 

11) 

15 

93 

34 

48 

63 

80 

08 

114 

88 

71 

55 

42 

29 

18 

11 

7 

7 

11 

18 

99 

42 

7.-, 

93 

98 

94 

77 

61 

46 

32 

20 

12 

6 

:, 

7 

14 

24 

37 

52 

70 

30 

114 

99 

83 

66 

50 

36 

23 

13 

7 

4 

5 

11 

20 

32 

47 

31 

131 

119 

105 

89 

71 

56 

40 

26 

16 

7 

3 

3 

8 

16 

27 

32 

145 

136 

1  2  ."> 

no 

04 

7G 

59 

43 

28 

16 

7 

3 

2 

5 

13 

33 

169 

148 

141 

131) 

115 

80 

82 

64 

47 

32 

1:1 

9 

3 

1 

4 

34 

153 

153 

151 

145 

134 

120 

104 

87 

6:1 

51 

35 

21 

11 

4 

1 

85 

14G 

152 

155 

154 

147 

137 

125 

no 

93 

74 

57 

40 

26 

14 

6 

3G 

134 

144 

159 

155 

154 

149 

141 

198 

114 

'.,7 

79 

61 

44 

2.1 

16 

37 

116 

130 

141 

150 

155 

155 

169 

144 

133 

119 

109 

85 

66 

49 

34 

38 

94 

III 

126 

13!) 

149 

155 

156 

153 

146 

137 

121 

107 

00 

72 

54 

39 

72 

90 

107 

123 

137 

147 

I.I 

156 

154 

148 

140 

127 

111 

95 

77 

40 

50 

66 

84 

101 

118 

132 

143 

152 

156 

156 

151 

142 

131 

116 

100 

41 

32 

46 

G2 

79 

97 

114 

128 

140 

14!) 

155 

155 

161 

144 

134 

121) 

42 

18 

28 

41 

57 

74 

92 

109 

194 

137 

146 

159 

154 

151 

146 

137 

43 

10 

15 

24 

37 

69 

68 

86 

103 

119 

133 

113 

150 

153 

159 

148 

44 

9 

8 

12 

21 

33 

48 

G4 

81 

98 

114 

128 

140 

147 

161 

161 

45 

14 

9 

8 

12 

19 

90 

43 

58 

75 

93 

109 

123 

136 

143 

14)1 

46 

25 

16 

10 

8 

10 

16 

26 

39 

54 

7,1 

87 

103 

118 

1311 

141) 

47 

43 

30 

19 

12 

9 

9 

15 

24 

36 

50 

81 

08 

113 

196 

48 

63 

47 

34 

23 

14 

10 

10 

13 

21 

31 

45 

60 

76 

106 

49 

86 

69 

53 

38 

26 

17 

12 

10 

13 

19 

29 

41 

55 

70 

86 

50 

107 

91 

74 

57 

42 

30 

20 

13 

11 

12 

17 

26 

37 

50 

(i.-, 

51    • 

127 

112 

07 

80 

63 

48 

35 

24 

17 

13 

13 

16 

24 

34 

46 

59 

142 

131) 

117 

102 

85 

68 

53 

39 

28 

20 

16 

15 

17 

31 

53 

161 

144 

134 

122 

106 

90 

74 

58 

44 

33 

23 

17 

18 

16 

91 

54 

155 

152 

147 

138 

126 

111 

96 

80 

64 

49 

37 

27 

21 

17 

17 

56 

150 

i:,:i 

152 

148 

140 

199 

117 

102 

86 

70 

56 

43 

33 

9J 

90 

140 

147 

151 

161 

147 

III 

139 

120 

106 

!>l 

76 

61 

1- 

37 

2- 

C7 

101 

!  II 

150 

151 

148 

113 

131 

124 

111 

97 

82 

G7 

54 

43 

Dtf 

58 

i  -  , 
103 

118 

131 

140 

146 

1  )'' 

149 

145 

138 

129 

117 

1113 

-  ' 

75 

80 

Rfll 

--j 

98 

113 

126 

137 

143 

148 

148 

146 

140 

132 

121 

06 

81 

«Jt' 

69 

61 

76 

92 

107 

121 

131 

13!) 

145 

148 

147 

142 

134 

198 

113 

UN) 

When  2->4d.7  is  subtracted  from  Arg.  I.,  add  19.6  to  Arg   XII. 


TABLE  XXXV. 


Perturbations  of  Log.  /•,  liy  Jupiter. 

Horizontal  Argument  =  I. 

Constant  added  30.            Period  of  Argument  1.,  224<i.7. 

Arg. 
XIII. 

d 

0 

d 

8 

16 

d 

24 

d 
32 

d 
40 

d 

48 

,1 
56 

i 

61 

.1 
72 

80 

d 

88 

d 

96 

d 

101 

112 

0 

81 

61 

46 

35 

23 

27 

31 

39 

50 

61 

72 

80 

85 

88 

83 

] 

100 

81 

62 

47 

35 

29 

28 

32 

39 

49 

60 

6!) 

76 

80 

83 

2 

119 

100 

80 

62 

46 

34 

23 

27 

31 

S8 

43 

57 

66 

72 

76 

3 

136 

119 

99 

7!) 

60 

44 

33 

27 

26 

30 

38 

46 

55 

63 

69 

4 

150 

136 

118 

97 

76 

57 

42 

31 

26 

25 

30 

37 

45 

54 

61 

5 

159 

149 

134 

115 

94 

73 

54 

39 

29 

24 

25 

29 

36 

45 

53 

6 

165 

160 

148 

132 

113 

90 

69 

50 

36 

27 

23 

24 

29 

37 

45 

7 

165 

165 

158 

145 

128 

107 

85 

64 

47 

33 

25 

22 

24 

30 

::s 

8 

161 

165 

163 

155 

141 

123 

102 

80 

60 

43 

31 

24 

23 

25 

32 

9 

153 

161 

164 

161 

151 

137 

117 

96 

75 

56 

40 

29 

24 

24 

23 

10 

14'i 

154 

160 

161 

157 

147 

131 

112 

91 

71 

52 

38 

29 

25 

26 

129 

142 

152 

158 

158 

153 

141 

.  125 

106 

86 

67 

50 

37 

30 

27 

12 

114 

127 

140 

149 

155 

154 

148 

136 

120 

101 

82 

63 

48 

37 

31 

13 

99 

112 

125 

138 

147 

151 

150 

143 

131 

115 

97 

78 

62 

48 

39 

14 

85 

96 

109 

123 

135 

143 

147 

146 

139 

127 

111 

94 

76 

61 

49 

15 

72 

82 

93 

107 

120 

132 

140 

144 

142 

135 

123 

108 

91 

75 

61 

16 

61 

67 

77 

90 

104 

118 

129 

138 

141 

139 

132 

121 

106 

90 

75 

17 

54 

56 

63 

74 

87 

101 

116 

128 

136 

140 

137 

130 

119 

104 

89 

18 

48 

48 

51 

59 

70 

84 

100 

114 

127 

135 

139 

136 

129 

113 

104 

19 

46 

42 

42 

46 

55 

67 

83 

99 

114 

127 

135 

138 

136 

128 

117 

20 

45 

39 

36 

37 

42 

52 

66 

82 

99 

115 

128 

136 

139 

136 

128 

21 

47 

39 

33 

31 

33 

39 

50 

66 

83 

101 

118 

130 

133 

140 

136 

22 

49 

40 

32 

27 

25 

2!) 

37 

50 

67 

86 

104 

121 

133 

140 

141 

23 

51 

43 

34 

27 

22 

21 

26 

36 

51 

70 

89 

108 

125 

136 

142 

24 

54 

47 

37 

28 

21 

18 

19 

26 

37 

54 

73 

94 

113 

129 

140 

25 

56 

49 

41 

32 

23 

17 

15 

18 

26 

40 

58 

78 

99 

118 

133 

26 

57 

53 

45 

37 

27 

19 

14 

14 

18 

29 

44 

63 

84 

105 

123 

27 

57 

55 

49 

42 

33 

24 

17 

13 

14 

20 

32 

49 

63 

90 

110 

23 

57 

56 

52 

46 

39 

30 

22 

15 

13 

15 

23 

37 

54 

74 

95 

29 

57 

56 

55 

51 

45 

37 

28 

20 

15 

14 

18 

27 

41 

59 

80 

30 

56 

57 

56 

54 

50 

44 

36 

27 

20 

16 

16 

21 

31 

46 

64 

31 

56 

57 

57 

57 

55 

50 

43 

35 

27 

21 

17 

18 

24 

35 

50 

32 

56 

56 

58 

59 

58 

56 

51 

44 

36 

28 

22 

19 

21 

27 

39 

33 

58 

58 

58 

60 

61 

61 

58 

52 

45 

37 

29 

23 

21 

23 

30  ' 

34 

62 

60 

59 

61 

63 

64 

64 

60 

54 

46 

37 

30 

24 

22 

24 

35 

67 

63 

62 

6:! 

65 

63 

69 

67 

63 

56 

47 

33 

30 

24 

22 

36 

74 

68 

65 

65 

67 

70 

72 

73 

71 

66 

58 

43 

39 

30 

24 

37 

83 

75 

70 

68 

70 

72 

76 

78 

77 

74 

63 

59 

49 

S3 

28 

38 

91 

83 

77 

73 

73 

75 

78 

82 

83 

82 

77 

70 

59 

48 

36 

39 

100 

91 

84 

80 

78 

79 

81 

85 

87 

88 

85 

80 

70 

59 

46 

40 

108 

100 

93 

87 

84 

83 

85 

88 

91 

93 

92 

88 

81 

70 

57 

41 

114 

108 

102 

95 

91 

89 

89 

91 

94 

97 

97 

96 

90 

81 

63 

42 

118 

115 

110 

104 

99 

95 

94 

95 

97 

100 

102 

102 

98 

91 

80 

43 

120 

120 

117 

112 

107 

102 

99 

99 

100 

102 

105 

106 

104 

99 

90 

44 

117 

122 

122 

119 

115 

110 

106 

104 

104 

105 

107 

109 

109 

106 

!lil 

45 

111 

120 

124 

124 

121 

117 

113 

109 

108 

108 

109 

111 

112 

111 

107 

46 

102 

115 

123 

126 

126 

123 

119 

115 

113 

111 

111 

112 

114 

114 

112 

47 

91 

108 

119 

126 

129 

128 

125 

121 

117 

114 

113 

113 

115 

116 

116 

43 

77 

96 

111 

122 

129 

131 

129 

126 

121 

117 

115 

114 

115 

116 

117 

49 

62 

82 

101 

115 

125 

131 

132 

129 

125 

121 

117 

115 

115 

116 

118 

50 

48 

69 

88 

105 

118 

127 

131 

131 

128 

124 

119 

116 

115 

115 

117 

51 

34 

53 

74 

93 

109 

121 

128 

131 

130 

126 

121 

117 

114 

113 

115 

52 

23 

40 

60 

79 

112 

122 

123 

129 

127 

122 

118 

114 

112 

112 

53 

16 

29 

46 

65 

84 

100 

113 

122 

126 

185 

122 

118 

113 

110 

110 

54 

12 

21 

34 

51 

69 

87 

102 

113 

120 

122 

121 

117 

112 

109 

107 

55 

14 

17 

26 

39 

56 

73 

89 

103 

112 

116 

117 

115 

111 

107 

104 

56 

20 

17 

21 

31 

44 

69 

75 

89 

101 

108 

112 

111 

109 

105 

102 

57 

30 

23 

21 

25 

34 

47 

61 

76 

89 

98 

104 

106 

105 

1D2 

9!) 

58 

44 

32 

25 

24 

23 

37 

49 

62 

76 

87 

95 

99 

100 

98 

96 

59 

62 

46 

34 

27 

26 

30 

39 

50 

62 

74 

84 

90 

93 

91 

92 

60 

81 

61 

46 

35 

23 

27 

31 

39 

50 

61 

72 

80 

85 

88 

88 

The  perturbations  are  in  units  of  the  eighth  decimal  place. 


TAI1L.K    XXXV. 


<;:* 


/'•  rt  nrlint  inns  «f  !,,><;.  r,  />//  .lii/n'/i  r. 

ll»ri/'Mital  Ar^iiiiifiit  =  1. 

<  ',,n-i.  -int  :nlilt  ,1  -  1                 Period  of  Arfum»nt  XIII.,  60  unit*. 

An 

MM 

120 

I2N 

.1 
130 

.1 
111 

,,, 

A 

100 

.1 
ION 

170 

1*1 

192 

200 

,:>, 

210 

»»l 

.1 

I) 

87 

86 

Hi 

105 

116 

190 

III 

150 

166 

156 

15  1 

ISO 

193 

1 

-•_' 

89 

-1 

80 

vt 

191 

135          117 

166 

11,1 

160 

152 

130 

2 

78 

7!) 

7H 

BO 

-1 

100 

II-.' 

196 

140 

l.vj 

n,  i 

103 

Ilil 

169 

3 

73 

75 

75 

77 

7:i 

-1 

09 

103 

116 

130 

ill 

150 

163 

11,5 

Mil 

4 

07 

70 

72 

73 

75 

70 

:u 

106 

r." 

134 

1  1- 

160 

165 

105 

5 

60 

05 

(;:i 

71 

7'.' 

71 

7!l 

86 

96 

rae 

193 

137 

150 

100 

105 

(i 

63 

0'! 

05 

i>- 

70 

71 

71 

70 

87 

96 

111 

125 

139 

151 

II,  I 

7 

4(i 

51 

05 

07 

60 

71 

71 

-  i 

-- 

09 

II-.' 

196 

1  I'l 

151 

B 

•10 

48 

56 

(,'J 

05 

i,- 

69 

71 

71 

-  i 

88 

00 

112 

196 

130 

9 

35 

43 

51 

58 

63 

66 

i,- 

69 

70 

73 

711 

87 

'.'- 

ill 

125 

10 

31 

38 

46 

51 

61 

65 

67 

66 

68 

60 

71 

77 

90 

109 

11 

:!n 

35 

43 

M 

58 

63 

66 

07 

66 

66 

66 

74 

82 

93 

19 

30 

34 

40 

47 

55 

61 

05 

07 

66 

ti.'i 

03 

63 

68 

70 

79 

13 

34 

34 

38 

45 

52 

50 

1,1 

66 

66 

01 

69 

58 

1,1 

65 

14 

41 

38 

39 

43 

50 

57 

02 

06 

66 

05 

i.-.' 

57 

54 

53 

55 

15 

50 

II 

42 

44 

48 

56 

61 

05 

66 

60 

62 

57 

52 

48 

47 

iii 

62 

52 

47 

46 

48 

53 

50 

63 

66 

66 

63 

52 

46 

42 

17 

75 

03 

64 

50 

50 

59 

57 

61 

05 

66 

01 

60 

53 

46 

40 

18 

89 

75 

64 

57 

53 

53 

56 

00 

(>:! 

65 

61 

55 

47 

40 

19 

103 

Ml 

76 

66 

59 

56 

66 

61 

64 

01 

69 

57 

50 

41 

20 

117 

103 

BB 

76 

67 

61 

68 

68 

60 

02 

62 

62 

52 

44 

21 

1  -.'-• 

116 

102 

88 

76 

67 

61 

5'.) 

50 

01 

01 

69 

60 

55 

47 

99 

137 

127 

115 

101 

87 

75 

07 

61 

59 

60 

61 

60 

56 

50 

23 

II-.' 

137 

l-.il  i 

113 

99 

85 

74 

66 

6D 

59 

.VI 

69 

59 

57 

53 

24 

144 

143 

136 

194 

110 

96 

83 

7-J 

64 

6!) 

58 

58 

58 

58 

55 

96 

142 

145 

142 

134 

121 

107 

B9 

7!) 

69 

62 

58 

57 

57 

57 

55 

26 

136 

144 

115 

141 

131 

li- 

103 

88 

75 

66 

i,i 

57 

66 

.51  i 

57 

27 

127 

138 

III 

111 

138 

127 

113 

oe 

84 

7'.' 

63 

5- 

56 

56 

66 

98 

114 

130 

Ml) 

144 

142 

134 

122 

KM 

93 

80 

68 

61 

57 

5(  i 

56 

29 

100 

118 

132 

140 

142 

1J9 

130 

117 

102 

88 

75 

65 

60 

57 

56 

30 

84 

103 

120 

132 

139 

140 

131 

194 

111 

98 

84 

72 

64 

59 

58 

31 

69 

88 

106 

121 

132 

137 

136 

130 

119 

106 

92 

80 

70 

63 

60 

54 

72 

90 

J07 

122 

131 

134 

139 

124 

114 

101 

89 

77 

O'.l 

64 

33 

41 

57 

71 

92 

108 

121 

128 

130 

127 

120 

109 

97 

86 

76 

69 

34 

43 

59 

75 

,    !>3 

108 

119 

126 

127 

123 

110 

106 

Hi 

BB 

76 

35 

25 

32 

41           59 

86 

92 

107 

117 

123 

123 

120 

113 

103 

93 

84 

30 

22 

24 

39 

44 

59 

76 

92 

105 

115 

120 

Ml 

117 

110 

102 

93 

37 

22 

20 

24 

31 

44 

59 

75 

!U 

104 

113 

119 

119 

116 

111! 

102 

38 

26 

20 

18 

22 

30 

43 

58 

75 

90 

103 

113 

118 

118 

116 

110 

39 

33 

23 

17 

16 

20 

29 

42 

58 

75 

90 

104 

113 

118 

119 

116 

40 

43 

30 

20 

14 

13 

17 

27 

42 

58 

75 

91 

105 

114 

119 

120 

41 

54 

39 

26 

15 

10 

10 

16 

27 

42 

59 

77 

03 

106 

116 

121 

42 

66 

50 

86 

21 

11 

6 

7 

15 

27 

43 

61 

80 

96 

no 

119 

43 

78 

62 

46 

30 

Hi 

7 

3 

6 

15 

28 

45 

01 

83 

100 

113 

44 

75 

59 

41 

25 

12 

1 

1 

6 

16 

31 

49 

69 

88 

mi 

45 

99 

87 

72 

54 

37 

21 

9 

2 

1 

6 

18 

34 

53 

74 

93 

46 

107 

97 

84 

68 

50 

33 

17 

6 

1 

1 

8 

21 

99 

59 

7:1 

47 

113 

106 

82 

65 

47 

2!) 

18 

5 

0 

3 

12 

20 

44 

65 

1- 

117 

113 

100 

94 

79 

62 

44 

27 

14 

5 

9 

6 

16 

31 

50 

49 

118 

117 

113 

105 

93 

78 

60 

42 

26 

13 

6 

4 

9 

21 

37 

50 

118 

120 

11!) 

114 

105 

go 

77 

59 

42 

26 

14 

8 

8 

14 

27 

51 

117 

120 

121 

120 

115 

106 

93 

76 

.V.I 

42 

26 

16 

11 

I-,' 

1!) 

5',' 

114 

118 

121 

123 

122 

116 

107 

93 

77 

59 

41 

28 

18 

M 

16 

63 

111 

115 

119 

123 

196 

124 

119 

109 

115 

78 

61 

44 

30 

21 

18 

54 

108 

111 

116 

122 

126 

129 

128 

122 

111 

H7 

80 

62 

45 

32 

24 

55 

104 

107 

112 

118 

125 

130 

133 

131 

125 

114 

9!) 

82 

64 

47 

34 

66 

100 

102 

106 

113 

121 

129 

135 

137 

136 

129 

117 

101 

83 

65 

49 

57 

97 

98 

101 

107 

116 

125 

134 

140 

113 

140 

132 

119 

103 

84 

66 

58 

94 

94 

101 

109 

119 

130 

139 

14(i 

148 

III 

136 

191 

lot 

88 

59 

90 

90 

91 

96 

102 

112 

194 

136 

1  Hi 

151 

159 

148 

138 

1  -.'•-' 

mi 

60 

87 

86 

86 

89 

96 

105 

no 

199 

III 

150 

156 

156 

150 

139 

193 

When  224*  .7  in  subtracted  from  Arg.  I.,  add  3.11  to  Arg.  XIII. 

TABLE  XXXVI. 


Perturbations  of  Log.  r,  by  Saturn. 

Horizontal  Argument  =  I. 

Constant  added  25.            Period  of  Argument  I.,  224<1.7. 

Aif. 
XIV. 

<l 
O 

,i 
§ 

d' 

16 

d 

24 

d 

32 

d 

40 

d 

48 

d 

56 

d 

64 

d 
72 

d 

SO 

d 

8§ 

d 

96 

d 

101 

d 

112 

0 

13 

8 

4 

1 

0 

0 

3 

6 

11 

17 

22 

27 

31 

35 

37 

1 

18 

13 

8 

4 

1 

0 

1 

3 

7 

12 

18 

23 

28 

32 

35 

2 

23 

18 

12 

7 

3 

1 

0 

1 

4 

9 

13 

18 

24 

28 

32 

3 

28 

22 

17 

11 

7 

3 

1 

1 

2 

5 

9 

14 

19 

24 

29 

4 

32 

27 

22 

10 

11 

6 

3 

1 

1 

3 

6 

10 

15 

20 

25 

5 

35 

31 

20 

21 

15 

10 

6 

3 

1 

2 

4 

7 

12 

10 

21 

6 

37 

34 

30 

25 

20 

15 

10 

0 

3 

2 

2 

5 

8 

13 

18 

7 

39 

36 

33 

29 

24 

19 

14 

9 

5 

3 

2 

3 

6 

9 

14 

8 

39 

38 

3G 

32 

28 

23 

18 

13 

8 

5 

3 

3 

4 

7 

11 

9 

39 

39 

37 

35 

32 

27 

22 

17 

12 

8 

5 

3 

3 

5 

8 

10 

39 

39 

38 

30 

34 

32 

26 

21 

16 

11 

8 

5 

4 

4 

G 

11 

38 

38 

38 

37 

30 

33 

29 

25 

20 

15 

11 

7 

5 

4 

5 

12 

37 

38 

38 

38 

36 

35 

32 

28 

24 

19 

14 

10 

7 

5 

4 

13 

37 

37 

37 

37 

37 

36 

34 

31 

27 

23 

18 

13 

9 

0 

5 

14 

37 

37 

37 

37 

37 

36 

35 

33 

30 

26 

21 

17 

12 

8 

6 

15 

37 

37 

37 

37 

37 

37 

30 

34 

32 

29 

25 

20 

15 

11 

8 

1C 

37 

37 

37 

37 

37 

37 

30 

35 

33 

31 

27 

23 

19 

14 

10 

17 

37 

37 

37 

37 

37 

37 

37 

36 

35 

33 

30 

26 

22 

17 

13 

18 

37 

38 

38 

37 

37 

37 

37 

36 

35 

34 

32 

29 

25 

20 

10 

19 

37 

38 

38 

38 

38 

37 

37 

37 

36 

35 

33 

31 

.  28 

24 

19 

20 

3G 

37 

38 

38 

38 

38 

38 

37 

37 

36 

35 

33 

30 

27 

22 

21 

34 

30 

38 

39 

39 

39 

38 

38 

37 

37 

3G 

34 

32 

29 

25 

2'j 

31 

35 

37 

39 

39 

39 

39 

38 

38 

37 

37 

30 

34 

32 

28 

23 

28 

32 

30 

38 

39  • 

40 

40 

39 

39 

38 

38 

37 

30 

34 

31 

24 

24 

29 

33 

30 

39 

40 

40 

40 

40 

39 

39 

38 

37 

35 

33 

25 

20 

25 

30 

34 

37 

39 

40 

40 

40 

40 

40 

39 

38 

37 

35 

20 

15 

20 

2G 

31 

35 

38 

39 

40 

41 

41 

40 

40 

39 

38 

37 

27 

10 

10 

21 

2G 

31 

35 

38 

40 

if 

41 

41 

41 

40 

40 

39 

28 

6 

11 

10 

22 

27 

32 

30 

39 

40 

41 

41 

41 

41 

40 

40 

29 

3 

7 

12 

17 

23 

28 

33 

3G 

39 

40 

41 

42 

41 

41 

41 

30 

1 

3 

7 

12 

18 

23 

29 

33 

37 

39 

41 

41 

42 

42 

41 

31 

0 

1 

3 

8 

13 

18 

24 

29 

34 

37 

39 

41 

41 

42 

42 

32 

0 

0 

1 

4 

8 

13 

19 

25 

30 

34 

37 

39 

41 

41 

42 

33 

2 

0 

0 

1 

4 

9 

14 

20 

25 

30 

34 

37 

39 

41 

42 

34 

5 

1 

0 

0 

2 

5 

10 

15 

21 

20 

31 

34 

37 

39 

41 

35 

9 

4 

1 

0 

0 

2 

6 

10 

16 

21 

27 

31 

35 

37 

39 

3G 

13 

8 

4 

1 

0 

0 

3 

0 

11 

17 

22 

27 

31 

35 

37 

The  perturbations  are  in  units  of  tlie  eighth  decimal  place. 

TABLE  XX XVI. 


PwCMrftotfoM  <>t  Lna.  r,  lnj  Saturn. 

Iliiri/unt.-i!  Ar;;il  ill  =  1 

Cmi-i.-uit  a.l.lrd  •,'.">.                          IVriuil  nf  Argument  XIV.,  'M  units. 

XIV 

ivto 

1 
I4N 

136 

lit 

1  >.• 

IOO 

d 
Hi* 

I7<i 

d 
1*11 

102 

200 

SON 

d 
-•Hi 

d 
tf-.il 

-•::•-> 

0 

• 

40 

•11 

41 

• 

4-> 

41 

41 

:!'.» 

:I7 

93 

28 

23 

17 

II 

1 

SI 

40 

II 

II 

M 

a 

II 

40 

3B 

36 

n 

H 

17 

2 

35 

37 

» 

40 

n 

41 

41 

41 

11 

40 

38 

36 

91 

27 

n 

3 

3d 

:!.-, 

:!7 

90 

:!'.i 

40 

41 

41 

41 

41 

40 

99 

35 

31 

26 

4 

29 

33 

35 

• 

• 

40 

40 

41 

41 

40 

39 

37 

34 

31 

:. 

•,>fi 

30 

33 

:r, 

:!7 

38 

40 

M 

40 

40 

40 

39 

37 

34 

(i 

a 

97 

n 

n 

36 

:i7 

38 

n 

18 

40 

40 

40 

40 

38 

96 

7 

in 

•a 

28 

n 

M 

86 

97 

9B 

n 

39 

40 

40 

88 

M 

8 

i:, 

20 

• 

•.*.) 

• 

31 

36 

37 

98 

39 

39 

89 

3D 

9 

tt 

17 

It 

26 

• 

n 

M 

36 

97 

97 

38 

38 

98 

38 

30 

10 

!t 

13 

18 

ti 

•.'7 

u 

33 

35 

36 

37 

37 

37 

ae 

:ts 

36 

11 

7 

10 

16 

19 

24 

IB 

:ii 

M 

35 

M 

37 

91 

37 

38 

38 

M 

5 

8 

12 

16 

21 

• 

29 

• 

M 

36 

36 

37 

37 

:(7 

37 

13 

I 

G 

9 

13 

18 

•,'•-> 

• 

30 

99 

98 

M 

36 

37 

37 

97 

11 

4 

5 

7 

10 

14 

19 

23 

28 

31 

34 

35 

36 

37 

37 

37 

15 

5 

4 

f> 

8 

11 

16 

20 

•-T. 

29 

:;•.' 

34 

3(i 

37 

37 

:t? 

1(1 

~      7 

B 

4 

I) 

9 

12 

17 

•.'1 

M 

30 

93 

35 

37 

91 

:<? 

17 

!» 

(i 

4 

1 

6 

1 

13 

18 

23 

27 

:ti 

34 

36 

37 

37 

18 

12 

8 

5 

4 

5 

7 

10 

14 

19 

24 

28 

32 

35 

37 

38 

1!) 

15 

10     . 

7 

5 

4 

5 

7 

11 

15 

20 

25 

30 

33 

3G 

37 

20 

18 

n 

9 

6 

4 

4 

5 

8 

12 

16 

22 

26 

31 

34 

36 

21 

21 

16 

12 

8 

5 

3 

3 

5 

8 

12 

17 

23 

28 

32 

86 

22 

24 

20 

15 

10 

7 

4 

3 

3 

5 

9 

13 

18 

M 

28 

33 

II 

27 

23 

19 

14 

9 

G 

:! 

2 

3 

5 

9 

14 

M 

• 

29 

•J4 

30 

27 

22 

17 

12 

8 

5 

2 

2 

3 

6 

10 

15 

20 

26 

II 

33 

30 

26 

21 

16 

11 

7 

4 

2 

1 

3 

6 

10 

16 

21 

26 

:c> 

33 

29 

25 

20 

1") 

10 

6 

3 

1 

1 

3 

6 

11 

16 

27 

37 

:!.-> 

Si 

89 

24 

19 

14 

9 

1 

2 

1 

1 

3 

7 

U 

28 

39 

37 

35 

32 

28 

23 

18 

13 

8 

4 

I 

0 

1 

3 

1 

29 

40 

39 

37 

35 

32 

27 

23 

17 

12 

7 

3 

1 

0 

1 

4 

30 

41 

40 

N 

37 

3T, 

31 

27 

22 

16 

11 

G 

2 

0 

0 

1 

31 

42 

41 

40 

39 

37 

35 

31 

36 

21 

16 

10 

5 

2 

0 

0 

32 

42 

42 

41 

41 

39 

37 

34 

30 

26 

20 

15 

9 

5 

1 

0 

ft 

42 

42 

1-' 

41 

41 

H 

n 

34 

30 

•A"> 

20 

14 

!) 

4 

1 

34 

41 

42 

• 

42 

41 

41 

39 

37 

34 

30 

24 

19 

13 

8 

4 

35 

40 

41 

42 

42 

42 

41 

41 

39 

37 

33 

29 

24 

18 

13 

7 

36 

39 

40 

41 

41 

42 

42 

41 

41 

39 

37 

33 

28 

23 

17 

12 

When  224-1.?  i«  nubtracted  from  Arg.  I.  add  0.8  to  Arg.  XIV. 

TABL.E  XXXVII. 


Perturbations  of  the  Latitude,  by  the  Earth. 

Horizontal  Argument  =  1. 

Constant  added  0".6->.         Period  of  Argument  I.,  224-1.7. 

Arg. 
XI. 

A 

0 

rl 

8 

rt 

16 

24 

ii 
32 

,i 
40 

a 
48 

d 

56 

d 

61 

d 

72 

d 

8O 

d 

88 

d 

96 

d 

101 

d 

112 

0 

48 

43 

39 

36 

34 

35 

37 

41 

45 

51 

58 

65 

71 

77 

81 

2 

.V, 

48 

42 

38 

35 

34 

34 

36 

40 

45 

50 

57 

64 

70 

75 

4 

62 

55 

48 

42 

38 

34 

33 

34 

36 

39 

44 

50 

56 

62 

68 

6 

70 

62 

55 

48 

43 

38 

3.-> 

34 

34 

36 

39 

44 

49 

55 

61 

8 

78 

70 

63 

55 

49 

43 

38 

36 

34 

34 

36 

40 

44 

49 

54 

10 

84 

77 

70 

62 

55 

4!l 

43 

39 

36 

35 

35 

37 

40 

44 

48 

12 

89 

83 

77 

69 

62 

55 

49 

44 

40 

37 

36 

36 

38 

40 

43 

14 

94 

89 

83 

76 

69 

62 

55 

49 

44 

40 

37 

36 

37 

38 

40 

16 

97 

93 

88 

82 

76 

69 

62 

55 

40 

44 

40 

38 

37 

36 

37 

18 

98 

96 

1(3 

88 

82 

76 

68 

62 

55 

49 

44 

41 

38 

36 

36 

20 

98 

97 

96 

92 

87 

82 

75 

69 

62 

G6 

50 

45 

41 

38 

36 

22 

96 

97 

97 

95 

92 

88 

82 

76 

69 

63 

56 

51 

45 

41 

38 

24 

92 

95 

96 

96 

95 

92 

88 

83 

77 

70 

64 

58 

51 

46 

41 

26 

86 

90 

93 

94 

95 

94 

92 

88 

84 

78 

72 

66 

59 

53 

47 

28 

78 

82 

87 

90 

92 

94 

93 

92 

89 

85 

80 

74 

68 

61 

55 

30 

69 

73 

78 

83 

87 

90 

91 

92 

91 

89 

86 

81 

76 

70 

64 

32 

60 

64 

69 

73 

78 

83 

87 

89 

91 

91 

89 

87 

83 

77 

73 

34 

52 

55 

59 

63 

68 

74 

79 

83 

87 

89 

90 

90 

88 

84 

80 

36 

47 

47 

50 

53 

58 

64 

69 

75 

80 

84 

87 

89 

90 

89 

86 

38 

44 

43 

43 

45 

48 

53 

59 

65 

71 

77 

81 

85 

88 

90 

89 

40 

4r> 

41 

:i!) 

38 

40 

43 

48 

54 

61 

67 

73 

79 

84 

88 

90 

42 

4S 

41 

37 

34 

34 

35 

39 

44 

51 

57 

64 

71 

78 

84 

88 

44 

W 

44 

38 

33 

30 

30 

32 

35 

41 

47 

55 

62 

70 

77 

83 

46 

59 

49 

41 

34 

29 

26 

26 

28 

32 

38 

45 

53 

61 

70 

77 

48 

67 

55 

45 

36 

29 

24 

22 

22 

25 

30 

36 

44 

52 

61 

70 

50 

75 

63 

51 

41 

32 

y.-> 

21 

18 

19 

22 

27 

35 

43 

52 

61 

52 

83 

71 

59 

47 

36 

27 

21 

17 

16 

17 

20 

26 

34 

42 

52 

54 

92 

80 

67 

55 

43 

32 

24 

18 

14 

13 

15 

19 

25 

33 

42 

56 

100 

88 

76 

63 

50 

39 

29 

21 

15 

12 

12 

14 

19 

25 

33 

58 

106 

96 

84 

72 

59 

47 

36 

27 

19 

14 

12 

12 

15 

19 

26 

60 

111 

102 

92 

81 

68 

56 

44 

34 

26 

19 

15 

13 

13 

16 

20 

62 

112 

106 

97 

87 

76 

65 

53 

43 

34 

26 

20 

16 

15 

15 

18 

64 

111 

107 

100 

92 

82 

72 

62 

52 

42 

35 

28 

23 

19 

18 

18 

66 

107 

104 

100 

94 

86 

77 

68 

60 

51 

43 

36 

30 

26 

24 

22 

68 

100 

100 

97 

93 

87 

80 

73 

65 

58 

51 

45 

39 

34 

32 

28 

71) 

93 

93 

92 

89 

85 

80 

75 

69 

63 

57 

52 

47 

42 

39 

35 

72 

84 

86 

86 

84 

82 

79 

75 

70 

66 

62 

58 

54 

50 

46 

43 

74 

76 

78 

7il 

79 

77 

75 

73 

70 

67 

64 

62 

59 

56 

53 

50 

76 

67 

70 

71 

72 

72 

71 

69 

68 

66 

65 

64 

62 

61 

59 

57 

78 

58 

62 

64 

66 

66 

66 

65 

65 

64 

65 

65 

64 

63 

63 

62 

80 

50 

54 

56 

59 

60 

61 

61 

61 

62 

63 

64 

65 

66 

67 

67 

82 

41 

45 

48 

51 

53 

55 

55 

57 

58 

60 

63 

65 

68 

69 

71 

84 

32 

36 

40 

43 

46 

48 

49 

51 

54 

57 

60 

64 

67 

71 

73 

86 

23 

28 

32 

35 

38 

40 

42 

45 

48 

52 

56 

61 

66 

70 

75 

88 

16 

20 

24 

28 

30 

33 

35 

38 

41 

45 

50 

56 

62 

67 

74 

00 

11 

15 

18 

21 

23 

26 

28 

30 

34 

38 

43 

50 

57 

64 

72 

!)2 

•8 

11 

13 

16 

18 

19 

21 

23 

26 

30 

36 

43 

50 

59 

67 

94 

7 

9 

11 

13 

14 

15 

16 

17 

20 

23 

28 

35 

42 

51 

60 

96 

9 

10 

II 

12 

12 

12 

13 

13 

14 

17 

21 

27 

34 

43 

53 

98 

13 

13 

13 

13 

13 

12 

11 

11 

11 

13 

15 

21 

27 

35 

45 

100 

19 

18 

17 

17 

16 

14 

12 

11 

10 

10 

12 

15 

21 

28 

37 

102 

25 

24 

23 

21 

20 

17 

15 

12 

10 

9 

10 

12 

16 

22 

31 

104 

33 

111 

30 

28 

25 

22 

19 

15 

13 

10 

9 

10 

13 

18 

25 

106 

42 

40 

38 

35 

32 

28 

25 

20 

16 

13 

10 

10 

11 

15 

21 

108 

51 

49 

47 

44 

40 

36 

32 

26 

21 

17 

13 

12 

11 

14 

18 

no 

61 

59 

57 

54 

50 

45 

40 

34 

28 

23 

18 

15 

13 

13 

16 

112 

70 

60 

67 

64 

61 

56 

50 

44 

37 

30 

24 

20 

16 

15 

16 

114 

78 

78 

76 

75 

72 

67 

62 

,->:> 

48 

40 

33 

27 

22 

19 

18 

116 

84 

85 

85 

85 

83 

Til 

74 

67 

6:1 

52 

44 

36 

30 

25 

23 

118 

86 

90 

92 

93 

92 

911 

86 

80 

72 

64 

66 

48 

40 

34 

30 

130 

85 

91 

95 

98 

99 

BO 

96 

91 

85 

77 

69 

60 

52 

45 

39 

The  perturbations  are  expressed  in  luiiidredtlis  of  a  second  of  arc. 


TABLE   XXXVII. 


/'.  •rliir/xiliini.-i  iifi/ir  Lntilitili\  liii  l/i-'  I'.m-ih. 

lli.riy.tmul  Argument  =  1. 

•  nit  .  -nl,  l-'tl                                 \'    :i.,il  ot'Ar;;iiiii.'iil  M.,  210  in. 

Arg.XI. 

.1 

a 
14N 

.1 
130 

.1 
111 

.1 

.1 
ION 

170 

INI 

194 

400 

40N 

9,« 

221 

2*4 

0 

85 

87 

-1 

Bl 

76 

70 

(il 

51 

46 

II 

37 

36 

•> 

BO 

,-i, 

86 

M! 

80 

71  i 

71 

86 

60 

to 

44 

II 

4 

73 

7fl 

Bl 

84 

•  1 

81 

71 

(i7 

66 

48 

G 

66 

71 

7". 

-l 

-  •• 

7' 

68 

lil 

00 

66 

8 

I.I 

7-J 

X 

79 

80 

80 

78 

7G 

74 

71 

67 

63 

10 

83 

57 

89 

66 

7  l 

7:! 

76 

7!) 

7  ' 

77 

75 

73 

70 

I-J 

47 

61 

63 

1,7 

71 

74 

76 

77 

71) 

7:1 

78 

77 

re 

1  1 

43 

li. 

88 

r,7 

I.I 

79 

7.-) 

7- 

79 

80 

81 

80 

16 

89 

41 

II 

61 

1,1 

71 

75 

81 

38 

18 

86 

37 

40 

HI 

l  . 

49 

58 

BB 

67 

~- 

76 

80 

20 

34 

86 

36 

37 

43 

47 

51 

86 

(il 

67 

73 

78 

BB 

86 

99 

86 

34 

BB 

BB 

86 

37 

40 

II 

49 

lil 

68 

71 

80 

86 

94 

37 

86 

n 

31 

81 

3'J 

34 

:t7 

49 

47 

54 

lil 

88 

7li 

83 

•JO 

49 

84 

81 

:ti 

86 

n 

46 

5:t 

iii 

70 

IB 

23 

4!) 

43 

N 

88 

29 

-7 

•Jii 

•J7 

23 

89 

38 

M 

52 

61 

71 

30 

87 

51 

44 

38 

33 

99 

26 

•Jl 

94 

27 

31 

86 

43 

52 

(i-J 

89 

GG 

60 

53 

4G 

3!) 

33 

•s, 

83 

98 

86 

88 

84 

43 

89 

34 

75 

68 

(i-J 

48 

II 

84 

29 

LT, 

93 

98 

B6 

86 

86 

44 

86 

83 

78 

79 

66 

r>7 

60 

42 

It:, 

26 

94 

88 

•J.-, 

31) 

36 

BH 

88 

85 

80 

74 

G7 

•"'•' 

52 

44 

37 

III 

•J7 

25 

•Jl 

26 

31 

40 

90 

BB 

87 

82 

n 

(i!) 

62 

54 

46 

33 

29 

26 

26 

23 

49 

BO 

U9 

Bl 

-- 

-  1 

73 

71 

63 

.'.;, 

1- 

41 

35 

31 

-.'- 

44 

83 

Bl 

89 

92 

85 

80 

73 

66 

.-,7 

50 

49 

1(7 

83 

30 

46 

-1 

89 

B9 

B4 

B3 

91 

87 

81 

74 

B7 

60 

51 

44 

89 

86 

43 

78 

84 

90 

94 

95 

B6 

88 

83 

76 

63 

46 

41 

50 

70 

78 

86 

!>l 

B6 

87 

87 

94 

90 

84 

77 

70 

62 

BB 

48 

69 

Gl 

71 

80 

B9 

B7 

DO 

93 

86 

89 

86 

7'.) 

7J 

Gl 

57 

52 

62 

79 

81 

88 

"i 

B8 

100 

100 

1  '7 

88 

87 

81 

7:1 

66 

r.(i 

43 

.'.:) 

63 

71! 

82 

BE 

BB 

Ml 

Ml 

B4 

89 

--.' 

75 

34 

43 

63 

73 

82 

90 

96 

BO 

Ml 

101 

08 

86 

90 

84 

GO 

•J7 

35 

44 

84 

G4 

73 

82 

90 

86 

99 

101 

101 

II!) 

96 

III 

88 

:i7 

45 

M 

lil 

73 

-1 

94 

97 

Mil 

101) 

B8 

86 

G! 

21 

86 

::•' 

38 

46 

66 

(il 

7-.' 

80 

83 

89 

BB 

BH 

98 

66 

•j;{ 

25 

2!) 

34 

40 

47 

66 

63 

71 

78 

84 

-:i 

93 

:i5 

96 

63 

27 

27 

39 

32 

3G 

I-J 

43 

66 

69 

69 

75 

81 

86 

89 

70 

83 

32 

32 

33 

36 

39 

44 

60 

55 

61 

67 

73 

78 

82 

86 

7'J 

40 

33 

87 

37 

37 

88 

42 

46 

68 

60 

BB 

70 

76 

7H 

74 

47 

45 

43 

41 

41 

41 

4'J 

44 

47 

50 

63 

67 

71 

76 

Efl 

49 

47 

46 

44 

44 

44 

18 

47 

60 

53 

67 

61 

65 

78 

61 

58 

56 

53 

51 

48 

47 

46 

45 

46 

47 

49 

52 

55 

59 

80 

66 

G5 

62 

59 

57 

64 

51 

48 

47 

46 

46 

46 

48 

80 

53 

83 

71 

70 

69 

66 

63 

56 

52 

49 

47 

45 

45 

45 

4G 

48 

84 

7.-, 

7:, 

79 

70 

66 

69 

57 

68 

49 

46 

45 

43 

43 

44 

86 

73 

-  ' 

80 

7!) 

77 

73 

68 

64 

54 

l  i 

46 

43 

41 

41 

88 

79 

84 

85 

83 

80 

76 

71 

68 

59 

54 

49 

45 

41 

39 

BO 

7- 

83 

gj 

89 

89 

87 

83 

7!) 

73 

66 

60 

54 

43 

44 

40 

89 

7.-, 

88 

87 

89 

92 

90 

81 

74 

67 

lil 

54 

48 

i-J 

'.il 

71) 

7- 

88 

Bl 

94 

96 

95 

'.••J 

-- 

B8 

7:, 

61 

64 

47 

72 

81 

88 

94 

93 

!I7 

'.'I 

89 

83 

77 

69 

Gl 

.",  1 

98 

55 

65 

75 

84 

91 

96 

99 

99 

BB 

90 

84 

77 

68 

62 

100 

47 

53 

78 

86 

93 

97 

100 

100 

B8 

90 

84 

77 

69 

1  1  i-J 

40 

61 

71 

81 

83 

94 

93 

100 

HID 

W 

B6 

80 

84 

77 

104 

43 

54 

64 

71 

83 

90 

88 

100 

iao 

98 

H4 

89 

-'. 

106 

37 

47 

57 

68 

77 

84 

91 

II!  1 

108 

100 

B7 

B4 

" 

103 

24 

89 

41 

51 

Gl 

70 

7'.) 

86 

96 

99 

100 

99 

97 

'.'3 

1  10 

21 

2s* 

36 

45 

54 

64 

7-J 

80 

96 

99 

99 

H 

96 

1  12 

19 

25 

31 

BB 

1- 

57 

66 

71 

-1 

87 

in) 

1  14 

•J  i 

23 

28 

86 

43 

61 

60 

G7 

71 

Bl 

Dl 

BB 

!>7 

116 

1  1  . 

22 

24 

28 

•J7 

::-J 

37 

46 
42 

63 

43 

(,  > 

67 

li) 

71 

66 

7-J 

P3 

87 

98 
M 

1  I  O 

190 

34 

33 

35 

37 

11 

45 

lil 

G!) 

74 

79 

84 

Wlicu  22-l''.7  li  subtracted  trom  Arg.  I.,  ;ulel  1  l/.UI  lo  Ary.  XI. 

11  V 


TABLE   XXX VJ  I. 


Perturbations  of  the  Latitude,  l>y  the  Earth. 

Horizontal  Argument  =  I. 

Constant  added  0".62.          Period  of  Argument  I.,  224J.7. 

Arg. 
XI. 

d 

o 

d 

% 

d 

16 

d 

24 

A 

32 

d 

40 

d 

48 

d 

56 

d 

61 

d 

72 

d 

80 

d 

§8 

96 

d 

104 

<i 
112 

120 

85 

91 

95 

93 

99 

99 

96 

91 

85 

77 

69 

60 

52 

45 

39 

122 

82 

89 

96 

100 

103 

105 

104 

101 

96 

89 

81 

73 

64 

57 

51 

124 

76 

85 

93 

99 

105 

108 

110 

108 

105 

99 

93 

85 

77 

70 

63 

126 

6'.) 

78 

88 

96 

103 

108 

112 

112 

111 

107 

102 

95 

88 

81 

75 

12si 

01 

71 

81 

91 

99 

106 

112 

114 

114 

112 

109 

104 

98 

92 

86 

130 

54 

64 

74 

•  84 

94 

103 

109 

113 

115 

115 

113 

109 

104 

100 

94 

132 

47 

57 

67 

77 

88 

97 

105 

no 

114 

116 

115 

113 

109 

106 

101 

134 

41 

50 

60 

70 

81 

ill 

99 

107 

112 

114 

115 

114 

112 

110 

106 

136 

36 

44 

53 

63 

74 

84 

94 

101 

108 

112 

114 

114 

113 

112 

110 

138 

32 

39 

47 

56 

67 

77 

87 

95 

103 

108 

111 

113 

113 

112 

111 

140 

29 

35 

41 

50 

•5!) 

70 

79 

89 

97 

102 

107 

110 

111 

111 

111 

142 

28 

32 

37 

44 

53 

62 

72 

81 

89 

96 

101 

105 

107 

109 

109 

144 

30 

30 

35 

40 

47 

56 

64 

73 

82 

89 

94 

99 

102 

105 

106 

146 

33 

32 

35 

38 

43 

50 

58 

66 

74 

81 

87 

92 

96 

98 

100 

148 

38 

37 

36 

38 

41 

47 

53 

60 

67 

73 

79 

84 

88 

91 

94 

150 

45 

43 

41 

41 

42 

46 

50 

55 

61 

67 

72 

76 

80 

84 

85 

152 

53 

5!) 

47 

45 

45 

47 

49 

53 

57 

62 

66 

6!) 

73 

77 

78 

151 

61 

57 

54 

51 

50 

50 

51 

53 

56 

59 

62 

64 

67 

69 

70 

156 

68 

Gl 

61 

58 

56 

55 

55 

55 

56 

58 

60 

61 

62 

63 

64 

158 

73 

71 

68 

65 

62 

61 

59 

59 

59 

59 

59 

59 

59 

59 

59 

160 

/  4 

7(i 

74 

72 

69 

67 

65 

63 

62 

61 

60 

59 

57 

56 

55 

162 

80 

80 

79 

77 

75 

73 

70 

68 

66 

63 

62 

59 

57 

54 

52 

164 

83 

83 

83 

83 

81 

79 

76 

74 

71 

68 

65 

61 

58 

54 

50 

166 

83 

86 

87 

87 

87 

85 

83 

80 

77 

73 

69 

64 

60 

54 

50 

168 

83 

87 

90 

91 

92 

91 

89 

87 

83 

79 

74 

63 

63 

56 

50 

170 

80 

86 

90 

94 

96 

96 

95 

94 

90 

86 

80 

74 

67 

60 

52 

172 

75 

83 

89 

94 

98 

100 

100 

100 

97 

93 

88 

81 

73 

65 

56 

174 

6!) 

77 

85 

92 

98 

102 

104 

105 

103 

100 

95 

89 

81 

72 

62 

176 

60 

70 

79 

87 

95 

101 

105 

108 

108 

106 

103 

97 

89 

80 

69 

178 

51 

61 

71 

80 

89 

97 

103 

108 

110 

110 

108 

104 

97 

88 

78 

180 

42 

52 

61 

72 

81 

91 

98 

105 

110 

112 

112 

109 

104 

96 

87 

182 

35 

43 

•  52 

62 

72 

82 

91 

99 

106 

110 

112 

111 

108 

102 

94 

184 

29 

35 

43 

52 

62 

72 

82 

91 

99 

105 

109 

111 

110 

106 

100 

186 

26 

31 

36 

44 

53 

62 

72 

82 

90 

98 

104 

107 

108 

107 

103 

188 

26 

28 

32 

38 

45 

53 

62 

72 

81 

89 

96 

101 

104 

106 

103 

190 

29 

28 

30 

34 

39 

46 

54 

62 

71 

80 

87 

94 

98 

101 

101 

192 

33 

31 

30 

32 

35 

40 

47 

54 

61 

70 

78 

85 

91 

94 

97 

194 

40 

35 

33 

32 

34 

37 

41 

46 

53 

61 

68 

75 

82 

87 

91 

196 

47 

41 

37 

35 

34 

35 

37 

41 

46 

52 

59 

66 

72 

78 

83 

198 

56 

48 

43 

39 

36 

35 

35 

37 

40 

45 

50 

56 

62 

68 

74 

200 

65 

57 

51 

45 

41 

38 

36 

35 

36 

39 

43 

47 

53 

59 

65 

202 

74 

67 

60 

53 

47 

42 

39 

36 

35 

35 

37 

40 

44 

49 

54 

204 

83 

76 

69 

62 

55 

49 

44 

39 

36 

34 

34 

35 

37 

41 

45 

206 

91 

85 

78 

71 

64 

58 

51 

45 

40 

37 

34 

33 

33 

35 

37 

208 

96 

92 

86 

80 

74 

67' 

61) 

53 

47 

42 

37 

33 

31 

31 

31 

210 

99 

96 

92 

88 

82 

76 

69 

62 

55 

49 

43 

37 

33 

30 

29 

212 

98 

97 

96 

93 

89 

84 

78 

72 

64 

58 

50 

44 

38 

33 

29 

214 

94 

96 

06 

95 

92 

89 

85 

79 

73 

67 

59 

52 

45 

38 

33 

216 

89 

91 

93 

94 

93 

92 

89 

86 

81 

75 

68  • 

61 

53 

46 

39 

218 

82 

85 

88 

90 

92 

92 

91 

89 

86 

81 

76 

69 

62 

55 

47 

220 

74 

78 

82 

85 

88 

90 

91 

91 

89 

86 

82 

77 

70 

63 

55 

222 

67 

71 

75 

79 

83 

86 

88 

90 

90 

89 

86 

82 

77 

70 

63 

224 

60 

64 

68 

73 

77 

81 

84 

87 

89 

89 

88 

86 

•82 

77 

70 

226 

55 

58 

62 

66 

71 

75 

80 

84 

87 

88 

89 

88 

86 

82 

76 

22« 

50 

52 

55 

60 

65 

69 

74 

79 

83 

86 

89 

89 

88 

86 

82 

230 

46 

47 

50 

54 

58 

63 

68 

74 

79 

83 

87 

89 

89 

88 

86 

232 

43 

43 

45 

48 

52 

57 

62 

68 

74 

79 

84 

87 

89 

90 

88 

234 

41 

40 

41 

43 

46 

50 

55 

61 

67 

73 

79 

83 

87 

89 

90 

236 

41 

39 

38 

39 

40 

44 

48 

54 

60 

66 

73 

79 

83 

87 

89 

238 

44 

40 

37 

36 

36 

39 

42 

47 

52 

59 

65 

72 

78 

83 

86 

240 

48 

43 

39 

36 

34 

35 

37 

41 

45 

51 

58 

65 

71 

77 

81 

The  perturbations  are  expressed  in  liundredtlis  of  a  second  of  arc. 


TABLE  XXXVII. 


<;*> 


Perturbation*  uf  //«•  Liiti/mli-,  /•//  ///<•  /•,'«/•/  A. 

lloriy.unt.il  Argument  =  I. 

Constant  added  0-.62.                     Peri  f  Ar,,,,,,,,,,  XI  ,  -10  „,„,.. 

Arg. 

.1 

.1 
12N 

.1 

.1 
1  II 

152 

100 

.1 
10* 

170 

INI 

.»* 

4 

200 

.1 
20* 

.1 
210 

221 

.1 

120 

36 

14 

S3 

35 

37 

41 

16 

10 

54 

(it 

60 

74 

7:' 

199 

4G 

43 

41 

41 

41 

43 

46 

47 

:,,i 

54 

61 

$6 

70 

75 

194 

54 

50 

48 

47 

47 

47 

48 

49 

51 

57 

Gl 

65 

196 

69 

65 

61 

58 

66 

54 

53 

59 

51 

51 

:,u 

50 

51 

66 

!•.>- 

-1 

76 

T- 

69 

67 

1,1 

69 

56 

54 

51 

49 

<8 

1- 

40 

130 

00 

86 

83 

77 

74 

71 

(It 

60 

56 

51 

47 

45 

it 

139 

98 

95 

99 

HO 

^7 

84 

-1 

77 

7:s 

68 

61 

55 

ia 

45 

49 

134 

104 

101 

90 

98 

96 

93 

'.'1 

87 

82 

76 

68 

69 

54 

47 

49 

136 

108 

107 

105 

101 

lo:t 

101 

!>9 

96 

91 

70 

61 

59 

15 

138 

111 

109 

IW 

109 

108 

108 

lor- 

104 

100 

94 

87 

78 

Gil 

59 

•111 

140 

111 

111 

ill 

112 

112 

112 

114 

111 

108 

103 

96 

87 

77 

67 

55 

149 

lio 

111) 

112 

113 

11  1 

116 

Il- 

IK; 

lit 

no 

mi 

96 

75 

63 

144 

107 

108 

lio 

113 

115 

117 

ll!) 

190 

11!) 

in; 

in 

103 

0! 

71 

146 

109 

lot 

107 

Illl 

113 

116 

119 

122 

1  ->-,' 

191 

117 

IK) 

109 

91 

7!) 

148 

96 

99 

102 

105 

109 

113 

117 

121 

123 

183 

121 

116 

109 

90 

150 

89 

91 

95 

98 

103 

108 

113 

118 

191 

123 

199 

119 

114 

106 

96 

169 

"1 

83 

86 

90 

95 

100 

!•  I. 

112 

117 

190 

121 

120 

117 

110 

102 

151 

79 

74 

77 

81 

86 

91 

97 

l"l 

110 

III 

117 

II- 

116 

112 

106 

156 

65 

66 

68 

71 

76 

81 

87 

94 

101 

106 

III 

113 

114 

111 

107 

158 

59 

59 

GO 

63 

66 

71 

77 

84 

90 

97 

102 

106 

108 

108 

105 

160 

51 

53 

53 

54 

57 

61 

.66 

73 

80 

86 

99 

97 

100 

101 

101 

169 

50 

48 

47 

48 

4!) 

53 

57 

63 

60 

7G 

98 

87 

91 

94 

94 

164 

47 

44 

49 

41 

42 

44 

48 

53 

59 

66 

7-j 

77 

B9 

-7 

166 

45 

41 

38 

36 

36 

37 

40 

44 

50 

56 

<)'.! 

68 

7:t 

77 

7!) 

168 

44 

38 

34 

31 

30 

30 

32 

36 

41 

46 

53 

51) 

64 

68 

71 

170 

45 

37 

32 

27 

24 

23 

24 

27 

32 

37 

43 

49 

55 

59 

G:! 

172 

47 

38 

31 

86 

SO 

18 

18 

19 

23 

28 

34 

40 

46 

51 

55 

171 

59 

41 

32 

24 

18 

14 

12 

12 

15 

1!) 

25 

30 

36 

•1- 

46 

176 

58 

47 

36 

26 

19 

12 

9 

7 

8 

11 

16 

22 

27 

:',:! 

::- 

178 

67 

54 

42 

31 

22 

14 

8 

5 

4 

6 

9 

14 

19 

•-it   ' 

89 

180 

75 

63 

50 

38 

27 

17 

10 

5 

2 

2 

4 

8 

12 

17 

21 

182 

84 

72 

59 

47 

35 

24 

15 

8 

3 

2 

2 

4 

7 

11 

15 

184 

91 

80 

G7 

56 

44 

32 

21 

13 

7 

5 

2 

3 

5 

7 

11 

186 

96 

87 

7G 

64 

52 

40 

99 

20 

13 

9 

5 

5 

5 

7 

0 

99 

99 

83 

72 

61 

49 

38 

28 

21 

14 

11 

8 

8 

8 

10 

190 

99 

94 

87 

78 

63 

58 

47 

37 

29 

22 

17 

14 

13 

12 

19 

199 

96 

94 

89 

82 

74 

65 

55 

45 

37 

30 

96 

21 

19 

17 

16 

194 

92 

99 

89 

84 

78 

71 

69 

53 

4G 

39 

33 

2!) 

26 

24 

89 

1% 

86 

88 

87 

85 

81 

75 

68 

60 

54 

48 

42 

38 

34 

it,' 

30 

198 

79 

82 

83 

83 

81 

77 

72 

67 

61 

56 

51 

47 

43 

40 

38 

200 

70 

74 

77 

79 

79 

78 

75 

71 

67 

G:! 

59 

55 

,VJ 

50 

47 

202 

69 

65 

69 

72 

74 

75 

75 

73 

71 

69 

66 

64 

G'J 

69 

57 

204 

50 

60 

64 

68 

70 

72 

73 

73 

73 

72 

71 

70 

68 

67 

206 

40- 

45 

50 

54 

59 

63 

67 

70 

7'J 

74 

75 

76 

76 

7? 

7(i 

208 

33 

36 

40 

45 

50 

54 

59 

64 

68 

72 

75 

78 

80 

83 

-1 

210 

28 

30 

32 

36 

40 

45 

50 

56 

61 

67 

7-> 

77 

81 

a". 

89 

212 

27 

26 

26 

29 

32 

36 

41 

47 

53 

60 

66 

73 

79 

90 

214 

28 

26 

24 

24 

85 

29 

33 

38 

44 

51 

59 

66 

74 

82 

216 

33 

28 

25 

23 

22 

83 

27 

31 

36 

43 

50 

58 

67 

76 

85 

218 

40 

34 

29 

25 

22 

21 

23 

25 

29 

35 

42 

51 

59 

69 

7:) 

220 

48 

41 

34 

29 

24 

22 

21 

22 

85 

29 

35 

43 

51 

61 

71 

56 

47 

41 

34 

28 

24 

22 

21 

22 

25 

30 

36 

45 

54 

'  1 

994 

63 

66 

48 

41 

34 

29 

25 

22 

22 

23 

86 

31 

38 

47 

57 

226 

70 

63 

55 

48 

40 

34 

29 

25 

23 

22 

24 

28 

33 

41 

50 

228 

76 

70 

63 

55 

47 

40 

34 

29 

25 

23 

23 

25 

30 

36 

44 

230 

81 

76 

69 

G'J 

54 

47 

40 

34 

29 

98 

24 

98 

27 

39 

939 

86 

81 

7G 

69 

69 

."•! 

47 

40 

34 

29 

26 

25 

26 

29 

34 

88 

86 

61 

76 

69 

62 

55 

47 

41 

34 

30 

28 

27 

88 

2:16 

89 

88 

86 

81 

76 

69 

69 

66 

48 

41 

3G 

39 

80 

:;i 

938 

-- 

89 

88 

86 

81 

76 

70 

63 

56 

49 

43 

38 

84 

240 

85 

87 

88 

87 

84 

81 

70 

70 

64 

57 

51 

46 

41 

37 

\Vhun  2-J4J.7  is  subtracted  from  Arg.  I.,  add  147.64  to  Arg.  XI. 


70 


TABLE   XXXVIII. 


Perturbations  of  the  Latitude,  by  Jupiter. 

Horizontal  Argument  =  1. 

Constant  added  0".'J1.          Period  of  Argument  I.,  234-1.7. 

Arg. 
Xlll. 

d 

0 

d 

8 

d 

10 

d 

21 

d 

a  a 

d 

40 

d 

48 

d 
56 

d       d 

61   73 

d 

§0 

d 

§8 

96 

101 

d 
113 

0 

17 

14 

11 

9 

7 

6 

5 

5 

6 

G 

8 

10 

12 

IS 

18 

1 

21 

18 

15 

12 

9 

7 

6 

5 

4 

5 

5 

7 

9 

12 

15 

2 

25 

22 

18 

15 

12 

9 

7 

5 

4 

4 

4 

5 

6 

9 

11 

3 

29 

2G 

22 

11) 

15 

12 

9 

7 

5 

4 

.  3 

3 

4 

6 

8 

4 

32 

29 

2G 

22 

19 

15 

12 

9 

G 

5 

3 

3 

3 

4 

6 

5 

35 

32 

29 

26 

22 

19 

15 

12 

9 

6 

4 

3 

3 

3 

4 

(i 

37 

35 

32 

29 

26 

22 

18 

15 

11 

8 

G 

4 

3 

3 

3 

7 

38 

37 

35 

39 

89 

20 

22 

18 

15 

11 

8 

G 

4 

3 

3 

8 

39 

38 

37 

34 

39 

29 

25 

22 

18 

11 

11 

9 

6 

6 

4 

9 

39 

38 

38 

36 

34 

31 

28 

25 

21 

18 

15 

12 

9 

7 

5 

10 

37 

38 

38 

37 

35 

33 

31 

28 

24 

21 

18 

15 

12 

10 

8 

11 

3G 

37 

37 

37 

36 

34 

32 

30 

27 

24 

21 

18 

15 

13 

11 

13 

33 

35 

36 

36 

36 

35 

34 

32 

30 

27 

24 

22 

19 

16 

14 

13 

30 

32 

34 

35 

35 

35 

34 

33 

31 

29 

27 

25 

22 

20 

17 

14 

27 

29 

31 

32 

33 

34 

34 

34 

33 

31 

29 

27 

25 

23 

21 

15 

23 

26 

28 

30 

31 

32 

33 

33 

33 

32 

31 

30 

28 

26 

24 

16 

20 

22 

25 

27 

•  28 

30 

31 

32 

33 

33 

32 

31 

30 

2!) 

27 

17 

17 

19 

21 

23 

25 

27 

29 

31 

32 

32 

33 

33 

32 

31 

30 

18 

14 

16 

18 

20 

22 

24 

27 

29 

30 

32 

33 

33 

33 

33 

32 

19 

11 

13 

15 

17 

19 

21 

24 

26 

28 

30 

32 

33 

34 

34 

34 

20 

9 

10 

12 

14 

1C 

18 

21 

23 

26 

28 

30 

32 

34 

34 

35 

21 

8 

8 

9 

11 

13 

is 

18 

20 

23 

26 

as 

31 

33 

34 

35 

22 

7. 

7 

7 

'.) 

10 

12 

15 

18 

20 

23 

26 

29 

32 

34 

35 

23 

7 

6 

6 

7 

8 

10 

12 

15 

18 

21 

24 

27 

30 

89 

34 

24 

7 

"  6 

5 

6 

6 

8 

10 

12 

15 

18 

21 

25 

28 

31 

33 

25 

8 

6 

5 

5 

5 

6 

8 

10 

13 

15 

19 

22 

25 

28 

31 

26 

9 

7 

6 

5 

5 

5 

6 

8 

10 

13 

16 

10 

23 

26 

29 

27 

11 

9 

7 

6 

5 

5 

5 

6 

& 

11 

14 

17 

20 

24 

27 

28 

14 

11 

8 

7 

5 

5 

5 

6 

i 

i) 

12 

15 

18 

21 

24 

29 

16 

13 

10 

8 

6 

5 

5 

5 

6 

8 

10 

12 

15 

18 

22 

30 

19 

16 

13 

10 

8 

6 

6 

5 

6 

7 

8 

10 

13 

16 

19 

31 

21 

18 

16 

12 

10 

8 

7 

6 

6 

6 

7 

9 

11 

14 

16 

32 

24 

21 

18 

15 

12 

10 

8 

7 

7 

6 

7 

8 

10 

12 

14 

33 

27 

24 

21 

18 

15 

13 

11 

9 

8 

7 

7 

7 

9 

10 

12 

34 

29 

26 

24 

21 

18 

15 

13 

11 

9 

8 

7 

7 

8 

9 

10 

35 

31 

29 

26 

24 

21 

18 

16 

14 

11 

10 

9 

8 

8 

8 

9 

36 

33 

31 

29 

27 

24 

22 

19 

16 

14 

12 

10 

9 

8 

7 

7 

37 

34 

33 

31 

30 

27 

25 

22 

19 

17 

14 

12 

10 

9 

8 

7 

38 

35 

34 

33 

32 

30 

28 

25 

23 

20 

17 

15 

12 

10 

8 

7 

39 

35 

35 

35 

34 

33 

31 

29 

26 

23 

20 

18 

15 

12 

10 

8 

40 

35 

36 

36 

36 

35 

34 

32 

29 

27 

24 

21 

17 

15 

12 

9 

41 

34 

35 

36 

37 

37 

36 

34 

32 

30 

27 

24 

20 

17 

14 

11 

42 

32 

34 

36 

37 

38 

38 

37 

35 

33 

30 

27 

24 

20 

17 

13 

43 

30 

33 

35 

37 

38 

39 

39 

37 

36 

33 

31 

27 

24 

•  20 

16 

44 

28 

31 

34 

36 

38 

39 

40 

39 

38 

36 

34 

30 

27 

23 

19 

45 

25 

28 

32 

35 

37 

39 

40 

40 

No 

39 

36 

34 

30 

26 

22 

46 

22 

25 

29 

33 

36 

38 

40 

41 

41 

40 

39 

36 

33 

30 

26 

47 

18 

22 

26 

30 

34 

37 

39 

41 

41 

41 

40 

38 

36 

33 

29 

48 

15 

19 

23 

27 

31 

35 

37 

40 

41 

41 

41 

40 

38 

35 

32 

49 

12 

16 

20 

24 

23 

32 

35 

38 

40 

41 

41 

41 

39 

37 

35 

50 

9 

12 

16 

20 

25 

28 

32 

35 

38 

40 

41 

41 

40 

39 

37 

5! 

6 

9 

13 

17 

21 

25 

29 

32 

35 

38 

39 

40 

40 

39 

38 

52 

5 

7 

10 

14 

17 

21 

25 

29 

32 

35 

37 

38 

39 

39 

39 

53 

4 

5 

8 

11 

11 

17 

21 

25 

28 

31 

34 

36 

38 

38 

38 

54 

3 

4 

6 

8 

11 

14 

17 

21 

24 

27 

30 

33 

35 

37 

38 

55 

4 

4 

5 

6 

8 

11 

14 

17 

20 

23 

27 

30 

32 

34 

36 

56 

5 

4 

4 

5 

7 

8 

11 

13 

16 

1!) 

23 

26 

28  . 

31 

33 

57 

7 

6 

5 

5 

5 

7 

8 

10 

13 

15 

18 

21 

21 

27 

30 

•  58 

10 

8 

G 

6 

5 

5 

6 

8 

1) 

12 

14 

17 

20 

23 

26 

59 

13 

II 

!) 

7 

6 

5 

5 

6 

7 

9 

11 

14 

16 

19 

22 

GO 

17 

14 

11 

9 

7 

6 

5 

5 

5 

G 

8 

10 

12 

15 

18 

'Die  perturbations  are  expressed  in  hundredtlis  of  a  second  of  arc. 


TA1IL.E   XXXVIII. 


Perturbations  «/  'the  La/Huilf,  Inj  ./<//<//.-;•. 

Cuii>l.iMl  aildi'd  II".  -'I.                        IV  rind  i>r  Ar»iinii-iil  M  II.,  l>i>  units. 

*  r,. 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

.1 

AFC. 

XIII. 

129 

131 

13.J 

100 

16* 

170 

1*1 

192 

200 

20* 

210 

1 

0 

89 

89 

81 

83 

35 

87 

36 

37 

36 

38 

39 

98 

98 

i 

IS 

81 

83 

31 

34 

36 

37 

38 

37 

35 

33 

80 

9 

II 

ia 

Jl 

93 

88 

31 

34 

36 

30 

37 

38 

33 

3 

II 

II 

17 

•Jl 

85 

31 

34 

36 

.:  i 

30 

30 

37 

35 

4 

- 

II 

14 

17 

81 

•j:, 

98 

37 

38 

30 

38 

37 

5 

6 

a 

II 

1  1 

18 

21 

95 

90 

39 

34 

37 

30 

39 

38 

(i 

1 

6 

8 

II 

II 

18 

89 

96 

39 

84 

36 

38 

36 

30 

7 

:! 

5 

(i 

g 

19 

15 

Id 

•J.-. 

•j  i 

32 

34 

36 

37 

38 

8 

I 

1 

5 

7 

9 

19 

IS 

10 

89 

96 

88 

31 

33 

36 

36 

0 

5 

1 

8 

(i 

8 

10 

13 

16 

10 

99 

95 

M 

30 

88 

34 

10 

6 

6 

6 

6 

7 

!) 

11 

19 

16 

19 

99 

21 

27 

39 

II 

9 

7 

7 

7 

7 

8 

9 

11 

13 

16 

18 

•Jl 

24 

26 

19 

19 

10 

B 

8 

8 

8 

8 

10 

U 

13 

18 

18 

90 

93 

85 

13 

15 

13 

11 

10 

g 

8 

8 

9 

10 

11 

13 

IS 

17 

10 

99 

14 

U 

16 

11 

19 

n 

10 

9 

9 

9 

10 

11 

12 

14 

16 

18 

16 

99 

19 

17 

15 

13 

19 

10 

16 

8 

9 

10 

10 

13 

13 

16 

Hi 

96 

83 

91 

18 

16 

n 

19 

11 

10 

B 

a 

9 

10 

11 

19 

17 

88 

86 

94 

19 

17 

16 

13 

11 

M 

9 

8 

8 

9 

H) 

Id 

31 

90 

27 

85 

99 

'-'  i 

17 

18 

13 

11 

9 

8 

8 

7 

8 

1!) 

89 

39 

30 

38 

26 

93 

20 

Id 

15 

13 

11 

9 

7 

7 

7 

20 

36 

34 

39 

31 

89 

96 

23 

30 

17 

IS 

13 

10 

8 

7 

(i 

•Jl 

36 

35 

:H 

33 

31 

89 

26 

8) 

90 

17 

II 

11 

8 

7 

6 

99 

36 

36 

36 

35 

83 

81 

39 

26 

23 

30 

16 

13 

II 

8 

7 

96 

86 

36 

37 

86 

36 

88 

31 

88 

36 

99 

H 

16 

13 

10 

H 

94 

35 

36 

37 

37 

37 

35 

33 

31 

38 

95 

*    33 

18 

18 

12 

9 

25 

34 

36 

37 

37 

37 

36 

35 

33 

30 

97 

94 

•Jl 

17 

14 

11 

26 

32 

34 

36 

37 

37 

37 

36 

34 

33 

39 

27 

2:i 

90 

17 

14 

27 

30 

39 

34 

36 

37 

37 

37 

36 

34 

31 

80 

98 

23 

19 

Hi 

96 

97 

30 

33 

88 

36 

37 

37 

36 

88 

89 

31 

98 

33 

10 

• 

25 

38 

30 

33 

35 

36 

36 

36 

36 

34 

32 

30 

37 

35 

21 

30 

22 

25 

38 

30 

33 

34 

35 

36 

36 

35 

34 

32 

30 

37 

•Jl 

31 

19 

22 

96 

30 

32 

34 

35 

35 

88 

34 

89 

31 

90 

27 

tt 

17 

I'.l 

99 

85 

99 

31) 

33 

33 

34 

35 

35 

84 

88 

31 

29 

33 

14 

17 

W 

89 

96 

27 

39 

31 

33 

34 

38 

34 

34 

i!:i 

31 

34 

M 

14 

16 

19 

33 

24 

37 

30 

31 

33 

34 

34 

34 

M 

33 

35 

10 

11 

13 

16 

18 

21 

34 

36 

39 

31 

32 

34 

34 

86 

34 

36 

8 

9 

11 

13 

15 

18 

31 

33 

36 

38 

31 

39 

34 

86 

35 

37 

7 

8 

9 

10 

19 

15 

17 

30 

93 

35 

38 

31 

83 

84 

88 

38 

6 

6 

7 

8 

ID 

11 

14 

17 

30 

98 

36 

28 

31 

33 

86 

39 

6 

6 

6 

6 

7 

9 

11 

13 

16 

19 

33 

26 

29 

33 

34 

40 

7 

6 

6 

4 

5 

6 

8 

10 

13 

16 

30 

23 

36 

30 

33 

41 

8 

6 

6 

4 

3 

4 

6 

7 

10 

13 

Hi 

90 

98 

37 

81 

4',' 

ID 

7 

5 

3 

3 

3 

3 

5 

7 

10 

13 

16 

80 

94 

98 

4:) 

19 

9 

6 

4 

3 

2 

3 

3 

4 

7 

10 

13 

17 

21 

25 

44 

15 

11 

8 

5 

3 

2 

1 

1 

3 

4 

7 

10 

14 

18 

99 

45 

18 

14 

10 

7 

4 

2 

I 

1 

1 

2 

4 

7 

11 

14 

18 

46 

89 

17 

13 

10 

6 

4 

3 

1 

0 

1 

3 

5 

8 

II 

15 

47 

95 

21 

17 

13 

9 

6 

3 

9 

1 

1 

'   1 

3 

5 

8 

19 

48 

88 

24 

30 

16 

19 

9 

6 

3 

3 

1 

I 

2 

4 

6 

11 

49 

31 

28 

34 

19 

15 

19 

8 

.6 

4 

2 

1 

2 

3 

4 

7 

10 

31 

31 

27 

98 

19 

M 

13 

9 

6 

4 

3 

2 

3 

3 

5 

51 

38 

30 

27 

93 

1!) 

16 

19 

9 

7 

5 

4 

3 

3 

4 

69 

37 

SB 

33 

30 

26 

23 

19 

Hi 

13 

10 

8 

6 

4 

4 

4 

63 

38 

37 

85 

33 

30 

27 

33 

20 

17 

II 

11 

9 

7 

6 

5 

38 

37 

36 

35 

33 

30 

37 

24 

31 

18 

15 

12 

10 

8 

6 

86 

37 

37 

37 

36 

88 

33 

3') 

28 

96 

19 

16 

13 

11 

8 

'     56 

35 

36 

37 

37 

36 

95 

33 

31 

90 

26 

23 

30 

17 

14 

11 

57 

:i'J 

34 

36 

36 

37 

•M 

35 

34 

89 

80 

37 

34 

21 

1- 

15 

53 

89 

84 

35 

36 

37 

37 

36 

98 

31 

38 

•J.-, 

99 

19 

60 

96 

29 

31 

34 

35 

37 

37 

:tr 

37 

86 

84 

89 

91 

36 

28 

31 

33 

96 

37 

38 

38 

37 

36 

35 

» 

39 

98 

When  234J.7  U  subtracted  from  Arg.  I.,  add  3.11  to  Arg.  Mil. 


TABL.E   XXXIX. 


Values,  for  tin'  li-^lnninif  of  l!n-  year,  of  Ji\,  A'v,  iV'1.,  ":nl  of  tlic  Arguments  of  Nutation,  for  Washington 
Mi'ttii  J\ovn  <f  Jan.  0  in  Common  Yearn  and  Jan.  1  in  Bissextile  Years. 

Year. 

A~x. 

K,. 

K* 

Log  /;x. 

Log  ky. 

Log  k... 

XV. 

XVI. 

0    /      // 

0     /     // 

o    /    // 

d 

a 

1750 

89  58  6.44 

1  20  53.89 

352  48  5.43 

9.9992934 

9.9595611 

9.6191304 

1504.7 

1.9 

1751 

6.48 

54.03 

3.51 

2933 

5033 

1202 

1869.7 

1.7 

17625. 

6.53 

64.17 

352  48  1.60 

2932 

5655 

1100 

2235.7 

2.4 

1753 

6.57 

54.31 

352  47  59.68 

2932 

5677 

0997 

2600.7 

2.2 

1751 

6.61 

54.45 

57.77 

2931 

5699 

0895 

29^5.7 

2.0 

1755 

6.05 

54.59 

55.86 

2931 

5722 

0793 

3330.7 

1.7 

17565. 

6.69 

51.73 

53.95 

2930 

5744 

0691 

3690.7 

2.5 

1757 

6.73 

54.87 

52.04 

2930 

5766 

0589 

4061.7 

2.2 

1758 

6.77 

55.00 

50.13 

2929 

5788 

0480 

4426.7 

2.0 

175!) 

6.81 

55.14 

48.22 

2928 

5810 

0384 

4791.7 

1.7 

17605. 

6.86 

55.28 

46.31 

'2928 

5832 

0282 

5157.7 

2.5 

1761 

6.91 

55.42 

44.40 

2927 

5854 

0180 

5522.7 

2.3 

170-2 

6.96 

55.56 

42.49 

2926 

5876 

9.0190077 

5887.7 

2.0 

17G3 

7.02 

55.70 

40.58 

2926 

5899 

9.6189975 

6252.7 

1.8 

17045. 

7.08 

55.84- 

38.68 

2925 

5921 

9873 

6618.7 

2.5 

17G5 

7.13 

55.97 

36.77 

2924 

5943 

9770 

185.5 

2.3 

1700 

7.18 

56.11 

34.87 

2923 

5965 

9668 

550.5 

2.0 

1707 

7.24 

56.25 

32.96 

2923 

5987 

9565 

915.5 

1.8 

17685. 

7.30 

56.39 

31.06 

2922 

6009 

9463 

1281.5 

2.6 

1709 

7.35 

56.52 

29.15 

2921 

6031 

9300 

1646.5 

2.3 

1770 

7.40 

56.66 

27.25 

2920 

6053 

9258 

2011.5 

2.1 

1771 

7.44 

56.80 

25.35 

2920 

6076 

9150 

2376.5 

1.8 

IT12B. 

7.48 

56.94 

23.44 

2919 

6098 

9053 

2742.5 

2.6 

1773 

7.5-2 

57.07 

21.54 

2919 

6120 

8951 

3107.5 

2.3 

1774 

7.57 

57.21 

19.64 

2918 

6142 

8848 

3472.5 

2.1 

1775 

7.61 

57.35 

17.74 

2918 

6164 

8740 

3837.5 

1.9 

17705. 

7.05 

57,18 

15.84 

2917 

6186 

8644 

4203.5 

2.6 

1777 

7.69 

57.62 

13.94 

2916 

6208 

8541 

4568.5 

2.4 

1778 

7.73 

57.75 

12.04 

2916 

6230 

8439 

4933.5 

2.1 

1779 

7.78 

57.89 

10.14 

2915 

6252 

8336 

5298.5 

1.9 

17805. 

7.83 

58.03 

8.24 

2914 

6275 

8234 

5664.5 

2.6 

1781 

7.88 

58.16 

6.31 

2914 

6297 

8132 

6029.5 

2.4 

1782 

7.94 

58.30 

4.44 

2913 

6319 

8029 

6394.5 

2.2 

1783 

8.00 

58.43 

2.54 

2912 

6341 

7927 

6759.5 

1.9 

17845. 

8.06 

58.57 

352  47  0.65 

2911 

6363 

7824 

327.2 

2.7 

1785 

8.11 

58.70 

352  46  58.75 

2911 

6385 

7722 

692.2 

2.4 

1780 

8.17 

58.84 

56.86 

2910 

6407 

7619 

1057.2 

2.2 

1787 

8.'23 

58.97 

64.96 

2909 

6429 

7517 

1422.2 

1.9 

17885. 

8.'28 

59.11 

53.07 

2909 

6452 

7414 

1788.2 

2.7 

1789 

8.32 

59.24 

51.17 

2908 

6474 

7312 

2153.2 

2.5 

1790 

8.36 

59.38 

49'.28 

2907 

6496 

7209 

2518.2 

2.2 

1791 

8.40 

59.51 

47.39 

2907 

6518 

7106 

2883.2 

2.0 

179:25. 

8.44 

59.64 

45.50 

2906 

6540 

7004 

3249.2 

2.7 

1793 

8.48 

59.78 

43.60 

2906 

6562 

6901 

3614.2 

2.5 

1794 

8.53 

1  26  59.91 

41.71 

2905 

6584 

6799 

3979.2 

2.2 

1795 

8.57 

1  27  0.05 

39.82 

2905 

6000 

6696 

4344.2 

2.0 

17905. 

8.61 

0.18 

37.93 

2901 

0029 

6593 

4710.2 

2.8 

1797 

8.05 

0.31 

36.01 

2903 

0651 

6491 

5075.2 

2.5 

1798 

8.70 

0.45 

34.15 

2903 

6673 

6388 

5440.2 

2.3 

1799 

89  58  8.70 

1  27  0.58 

352  46  32.26 

9.9992902 

9.9596695 

9.6  180286 

5805.2 

2.0 

i  c:ii-li  of  llin  <iuuntitic.s  A"x.,  ATy  and  K2  the  constant  2J".00  has  l>.'.-u  :;ul>tr;irt.'il ;  uiiil  from  log  A-y  tlie  constant  0.0000089, 

and  from  log  k,  tliu  constant  U.UOOOuUi) 


TA11L.K    X\\I\. 


\'nliii:i,fiir  the  l»-  <>  hi  n  in*  of  tin-  iii-fir.  »/'  A',.  A",.  A-'-.,  ami  of  tin-  An;iiiiiciii.t  of  I\'iilii!i,ni,f,ir  U'tmhiiigloH 

:   .\nnii  iif'.ltiii.  0  /;/   Cniii/iion    \Vii;'.v  mill  .Inn.   1   I/I   Iiit.-n.iti/,-    i'lvirv. 

Year. 

A\. 

K,. 

A'. 

Log  A\. 

Log  Ay 

Log  i-,. 

XV. 

XVI. 

0          /           // 

0          /           '/ 

0          /           II 

d 

il 

1800 

89    5N      N.NV! 

1  27     0.71 

K.VJ  i<;  :t(t.:57 

!t.:i!l!l2!)01 

!>.!l.-»96717 

9.61861S.-J 

6170.2 

l.s 

1801 

0.84 

2S.  IS 

2900 

6739 

6080 

6:>35.2 

1.5 

1802 

8.98 

0.98 

•^(i.r.ii 

2900 

6761 

5978 

102.0 

l.:( 

1803 

8.98 

.11 

24.70 

2899 

6783 

6876 

467.0 

1.0 

1804J3. 

!U)1 

.24 

32.81 

2898 

6806 

5778 

S33.0 

1.8 

1805 

9.09 

.:!7 

20.93 

2897 

6828 

5670 

llit.N.O 

1.6 

1S06 

9.16 

.51 

19.04 

2897 

6850 

5667 

1563.0 

1.3 

1807 

9.80 

.64 

17.16 

2896 

6872 

5  16  1 

lifJN.O 

1.1 

isos/;. 

9.2  1 

.77 

15^7 

2896 

UN!)  1 

.r.:!(W 

2-J!M.<) 

1.8 

1S01) 

9.2!) 

.90 

18.89 

2895 

6916 

6259 

•j<;:.!).o 

1.6 

1H10 

9.88 

t>.():t 

11.50 

2894 

6889 

5156 

30v!  1.0 

1.1 

1H11 

9.31 

2.  Hi 

9.ea 

2894 

6961 

5053 

33N9.0 

1.1 

isiae. 

!>.  1  1 

•..'.:{<> 

7.71 

2898 

6983 

4950 

3755.0 

1.9 

1813 

:>.  ir> 

iU3 

:•>:. 

2898 

7015 

4848 

4120.0 

1.6 

1814 

9.19 

8.56 

3.97 

2892 

•  7037 

4745 

1  1S.-..0 

1.1 

1818 

!t.;>3 

2.69 

2.09 

2892 

7059 

4642 

4850.0 

1.1 

18  Hi/;. 

9.58 

2.82 

.•i.'.-J  -16     0.21 

2891 

7082 

4539 

5216.0 

1.!) 

1817 

9.63 

ZJ95 

:i.vj  i.-)  r»s.:j3 

2890 

7101 

4436 

5581.0 

1.7 

9.69 

:{.os 

56.45 

2890 

7  rj<i 

i:c(  I 

5!)  16.0 

1.1 

1819 

9.75 

:{.-Jl 

51.57 

2889 

7148 

4381 

6311.0 

1.2 

18207?. 

9.80 

:).:u 

52.69 

2S8S 

7170 

4128 

6677.0 

1.9 

1821 

9.85 

:{,I7 

50.81 

2887 

7192 

4025 

2  13.7 

1.7 

1822 

!).!)! 

3.60 

48.93 

•JNN- 

7215 

8922 

608.7 

1.4 

1823 

!).!)7 

:t.7.'{ 

47.06 

2886 

7287 

3820 

973.7 

1.2 

1824A 

10.03 

3.86 

45.18 

2SS5 

7380 

3717 

1339.7 

2.0 

182S 

10.08 

3.99 

43.30 

2885 

7281 

3614 

1704.7 

1.7 

1826 

10.18 

4.12 

41.43 

2884 

7:to:i 

3511 

2069.7 

1.5 

1827 

11.17 

L35 

39.55 

•jss:{ 

7825 

3  ION 

2434.7 

1.2 

1S28#. 

10.21 

4.38 

37.68 

•jss:t 

7.'5  17 

3305 

2800.7 

2.0 

1829 

10.25 

4.51 

35.80 

•^ss-^ 

7570 

8208 

3165.7 

1.7 

1830 

10.29 

4.63 

33.93 

•Jss-> 

7899 

3099 

3530.7 

1.5 

1881 

10.33 

4.76 

32.06 

•Jssi 

7414 

2996 

3805.7 

1.3 

18335. 

K).:i7 

4.89 

30.19 

2881 

713G 

2893 

1281.7 

2.0 

1833 

10.42 

5.02 

28.31 

2880 

7  i:.s 

2790 

4626.7 

1.8 

1834 

10.16 

.      5.15 

26.44 

2879 

7480 

MB? 

4991.7 

1.5 

1835 

lO.r.  1 

5.28 

•J  1.57 

2879 

7503 

2584 

5356.7 

1.3 

1836  B. 

10.57 

5.40 

22.70 

2878 

7525 

2481 

5722.7 

2.0 

1837 

10.62 

5.53 

20.83 

2877 

784S 

2878 

lids-;.-; 

l.N 

1838 

10.68 

5.66 

18.96 

2877 

7569 

2275 

(i  152.7 

1.6 

1839 

10.73 

5.79 

17.09 

2876 

7591 

2172 

19.4 

1.3 

1840B. 

10.78 

5.91 

15.22 

2875 

7613 

2069 

385.4 

2.1 

1M1 

10.84 

6.04 

18,86 

2875 

7636 

1966 

750.4 

1.8 

1842 

10.90 

6.17 

11.48 

2874 

7668 

1863 

1115.4 

1.6 

IN  13 

10.95 

6.30 

9.62 

2873 

7  CM) 

1760 

1480.4 

1.3 

18442?. 

11.01 

6.42 

7.75 

2872 

7702 

1657 

1846.4 

2.1 

1845 

11.06 

6.55 

5.88 

2872 

7784 

I.V.I 

2211.4 

1.9 

is  Hi 

11.10 

6.67 

4.01 

2871 

7746 

lir.i 

2576.4 

1.6 

1847 

11.14 

6.80 

2.15 

2871 

7769 

1848 

2911.4 

1.4 

18482?. 

11.18 

6.93 

:i.vj   15    0.28 

2870 

7791 

1245 

3307.4 

2.1 

1849 

89  58  11.22 

1  27     7.05 

3.VJ  -14  58.42 

9.9992870 

9.9597  M3 

9.6181112 

36V..!.  1 

1.9 

From  each  of  the  quantities  Kx,  h\  anil  A'z,  <<"'  ••i.nslant  ','H"  no  !,;,<   I,,-.  „   sirlnr.-i.-tnl  ;   ami  IVum  log  /.,.  the  cunslant  O.OOOOOS'J, 
ami  from  lug  /.,  the  constant  0.0000560. 

74 


TABLE   XXXIX. 


Values,  for  the  beginning  of  ///<•  i/nir,  of  K^  7iv,  <^c.,  and  of  the  Arguments  of  Nutation,  for  Washington 
Mean  Noon  of  Jan.  0  in  Common  Years  and  Jan.  1  in  Bissextile  Years. 

Year. 

AV 

A',.        Kv 

Log  k*. 

Log  ks. 

Log  kz. 

XV. 

XVI. 

o    /     II 

0     /     // 

a    1    II 

a 

a 

1850 

89  58  11.27 

1  27  7.18 

352  44  56.55 

9.9992869 

9.9597825 

9.6181039 

4037.4 

1.6 

1851 

11.31 

7.31  i       54.69 

2869 

7847 

0936 

4402.4 

1.4 

18525. 

11.35 

7.13 

52.83 

2868 

7869 

0833 

4768.4 

2.2 

1858 

11.40 

7.56 

50.96 

2867 

7891 

0729 

5133.4 

1.9 

1854 

11.44 

7.68 

49.10 

2867 

7914 

0626 

5198,4 

1.7 

1855 

11.50 

7.81 

47.24 

2866 

7936 

0523 

5863,4 

1.4 

18565. 

11.56 

7.93 

45.38 

2865 

7958 

0420 

6229,1 

2.2 

1857 

11.63 

8.08 

43.52 

2865 

7980 

0317 

6591.4 

1.9 

1858 

11.67 

8.18 

41.66 

2864 

8002 

0213 

161.2 

1.7 

185!) 

11.73 

8.31 

39.80 

2863 

8021 

0110 

526.2 

1.5 

18(501?. 

11.79 

8.43 

37.94 

2863 

8046 

9.6180007 

892.2 

2.2 

1801 

11.81 

8.5(5 

36.08 

2862 

8069 

9.6179904 

1257.2 

2.0 

1862 

11.89 

8.68 

3  1.22 

2861 

8091 

9801 

1622.2 

1.7 

1863 

11.91 

8.80 

32.37 

2861 

8113 

9697 

1987.2 

1.5 

18645. 

11.99 

8.93- 

30.51 

2860 

8135 

9594 

2353.2 

2.2 

18(55 

12.03 

9.05 

28.65 

2859 

8157 

9491 

2718.2 

2.0 

1866 

12.07 

9.18 

26.79 

2859 

8179 

9388 

3083.2 

1.8 

18(57 

12.11 

9.30 

24.94 

2858 

8201 

9285 

3448.2 

1.5 

18685. 

12.15 

9.42 

23.08 

2858 

8224 

9181 

3814.2 

2.3 

1869 

12.19 

9.55 

21.23 

2857 

8246 

9078 

4179.2 

2.0 

1870 

12.24 

9.67 

19.37 

2857 

8268 

8975 

4544.2 

1.8 

1871 

12.28 

9.79 

17.52 

2856 

8290 

8872 

4909.2 

1.5 

18725. 

12.33 

9.92 

15.67 

2856 

8312 

8768 

5275.2 

2.3 

1873 

12.39 

10.04 

13.81 

2855 

8334 

8665 

56  10.2 

2.1 

1874 

12.44 

10.16 

11.96 

2854 

8356 

8561 

6005.2 

1.8 

1875 

12.50 

10.28 

10.11 

2854 

8378 

8458 

6370.2 

1.6 

187(55. 

12.56 

10.40 

8.26 

2853 

8401 

8355 

6736.2 

2.3 

1877 

•   12.62 

10.53 

6.41 

2852 

8423 

8251 

302.9 

2.1 

1878 

12.67 

10.65 

4.56 

2851 

8445 

8148 

667.9 

1.8 

1879 

12.73 

10.77 

2.71 

2851 

8467 

8044 

1032.9 

1.6 

18805. 

12.78 

10.89 

352  44  0.86 

2850 

8489 

7941 

1398.9 

2.4 

1881 

12.83 

11.01 

352  43  59.01 

2849 

8511 

7838 

1763.9 

2.1 

1882 

12.88 

11.14 

57.16 

2849 

8533 

7734 

2128.9 

1.9 

1883 

12.93 

11.26 

55.32 

2848 

8556 

7631 

2493.9 

1.6 

18845. 

12.97 

11.38 

53.47 

2848 

8578 

.  7528 

2859.9 

2.4 

1885 

13.01 

11.50 

51.62 

.2847 

8600 

7121 

3224.9 

2.1 

1886 

13.05 

11.62 

49.77 

2847 

8622 

7321 

3589.9 

1.9 

1887 

13.09 

11.71 

47.93 

2846 

8644 

7217 

395  1.9 

1.7 

18885. 

13.13 

11.86 

46.08 

2846 

8666 

7114 

4330.9 

2.4 

1889 

13.18 

11.98 

44.24 

2815 

8688 

7010 

4685.9 

2.2 

1890 

13.22 

12.10 

42.39 

2844 

8711 

6907 

5050.9 

1.9 

1891 

13.27 

12.22 

40.55 

2844 

8733 

6S01 

5115.9 

1.7 

.  189-25. 

13.33 

12.84 

38.71 

28  13 

8755. 

6700 

5781.9 

2.4 

1893 

13.39 

12,16 

36.86 

2812 

8777 

6597 

6146.9 

2.2 

1894 

13.45 

12.58 

35.02 

2842 

8799 

6493 

6511.9 

2.0 

1895 

13.50 

12.70 

33.18 

2811 

8821 

6390 

78.6 

1.7 

18965. 

13.56 

12.82 

31.34 

2840 

8843 

6286 

111.6 

2.5 

1897 

13.62 

12.!)  1 

29.50 

2840 

8866 

61  S3 

809.6 

2.2 

1898 

13.07 

13.06 

27.66 

8888 

6079 

111  1.6 

2.0 

1899 

89  58  13.73 

1  27  13.18 

352  13  25.82 

9.9992838 

9.9598910 

9.6175976 

1539.6 

1.7 

1'ruin  each  oftlic  quantities  /vV,  /v'y  ami  k",  tin;  constant  'i  I".')!)  h.i  .  been    laliirarti.'cl  ;  and  from  lo£  hy  thu  constant  0.0000089, 

and  from  lu;_'  /.'.,  the  constant  0.0000500 


TABLE    \V\I\. 


75 


Vn/iir.f,  fur  III''  tii-iji  luting  nl   l/i:'  i/i-iir.  i'/'  A"  .  A",.  iVr.,  mi'.'                              nU  «/'  \i</iiliuii,  far   \\'<i*hi,. 
;  .Von;/  n/'  Jim.  0  /;i   ('nut/nun    \<<ir«  ii/nl  Jim.   1  in  JJi 

Fear. 

A', 

A', 

A  . 

**. 

fry 

XV. 

\\l. 

o         /         /' 

0            /            // 

a        1        II 

,i 

d 

1900 

89  5S   13.78 

1  27   13.30 

3.VJ    13  -J:t.9s 

9.999-JS3S 

9.959,s!»:!2 

9.617:.^: 

1904.6 

1.5 

1901 

13.S-,; 

18.42 

•J-4.1  1 

2S37 

6954 

57  (is 

2269.6 

1.3 

1902 

18.87 

18.54 

20.30 

2881 

8976 

5665 

263  1.6 

1.0 

1903 

13.91 

13.65 

is.  17 

2836 

8998 

55(i  1 

2999.6 

0.8 

1904B. 

18.95 

13.77 

16.68 

MB! 

5458 

3365.6 

1.5 

1  !)().-> 

13.99 

13.89 

1  1.79 

2835 

9048 

535  1 

3730.6 

1.3 

1906 

1  1.03 

14.01 

12.96 

2835 

9065 

5250 

4095.6 

1.0 

1907 

1  1.08 

14.13 

11.12 

•JS3  1 

9081 

5117 

4460.6 

O.s 

1908B. 

1  1.12 

1  I.-J5 

9.28 

9109 

5013 

4826.6 

1.6 

1909 

11.17 

14.36 

7.  15 

2838 

9131 

1940 

5191.6 

1.3 

1910 

14J22 

11.  is 

5.61 

2832 

9154 

4886 

5556.6 

1.1 

1911 

1  l.'JS 

14.60 

3.78 

2832 

9176 

4732 

5921.6 

O.S 

1912#. 

14.3  1 

1  1.7-4 

1.95 

2831 

9198 

4629 

6287.6 

1.6 

1913 

11.10 

1  IX! 

352  43     0.11 

2830 

9220 

1525 

6652.6 

1.3 

1914 

1  1.  15 

14.95 

352  42  58.28 

2829 

9','  1;.' 

1  l-j-.' 

219.4 

1.1 

1915 

14.50 

15.07 

66.40 

2829 

9-ji;  i 

4318 

584.4 

0.9 

19167A 

14.56 

15.18 

54.62 

2828 

9287 

4214 

950.  1 

l.li 

1917 

14.62 

15.30 

52.79 

2827 

9309 

4110 

1815.4 

1.4 

1!)1H 

14.67 

15.48 

50.96 

2827 

9331 

4007 

1680.4 

1.1 

1919 

1  1.72 

15.53 

49.13 

289i 

9353 

8908 

2045.4 

0.9 

1920//. 

14.76 

15.65 

47.30 

2826 

9375 

3799 

2411.4 

1.6 

19-J1 

14.80 

15.76 

45.47 

2825 

9397 

3695 

277(i.  t 

1.4 

l!fJ-^ 

1  1.8  1 

15.88 

43.64 

2825 

9420 

3591 

8141.4 

1.2 

1923 

14.88 

16.00 

41.82 

•_>vj  1 

9442 

8488 

8506.4 

0.9 

jtSMB. 

14.93 

16.11 

39.99 

2824 

9464 

3384 

3872.  1 

1.7 

1  !>-,'.-> 

14.97 

16.28 

38.16 

2823 

9486 

3280 

4237.  1 

1.1 

1926 

16.03 

16.34 

36.33 

2823 

9508 

3176 

4602.4 

1.2 

19:27 

15.06 

16.46 

34.51 

2822 

9530 

3072 

4967.4 

0.9 

19283. 

15.11 

16.57 

32.68 

2821 

9552 

2969 

5333.  1 

1.7 

1929 

15.17 

16.69 

30.86 

2821 

9575 

2865 

5698.4 

1.5 

1930 

15.22 

16.80 

29.03 

2820 

9597 

2761 

6063.  1 

U2 

1931 

15.28 

16.92 

27.21 

2819 

9619 

2657 

6428.4 

1.0 

19325. 

15.31 

17.03 

25.38 

2819 

9611 

2553 

6794.4 

1.7 

l!t:t:i 

15,10 

17.14 

23.56 

2818 

9663 

2450 

361.1 

1.5 

1934 

15.46 

17.26 

21.73 

2817 

9685 

23  Hi 

726.1 

1.3 

1935 

15.51 

17.37 

19.91 

2817 

9708 

2-J  I'J 

1091.1 

1.0 

1986JB. 

15.57 

17.49 

18.09 

2816 

9730 

2188 

1457.1 

1.8 

1937 

15.62 

17.60 

16.27 

2815 

9752 

203  1 

1822.1 

us 

1938 

15.66 

17.71 

14.45 

2815 

9774 

1930 

2187.1 

1.3 

1939 

15.71 

17.83 

12.63 

2814 

9796 

1826 

2552.  1 

1.0 

1940B. 

15.75 

17.94 

10.81 

2814 

9818 

1722 

2918.1 

1.8 

1911 

15.79 

18.05 

8.99 

2813 

9841 

1618 

3v>s3.  1 

1.6 

194-2 

15.83 

18.17 

7.17 

2813 

9863 

1514 

3648.1 

1.3 

1943 

15.88 

18.28 

5.36 

2812 

9885 

1410 

4013.1 

1.1 

19445. 

15.92 

18.39 

3.54 

2812 

9907 

1306 

1379.1 

1.8 

1915 

15.97 

18.50 

352  42     1.72 

2811 

9929 

1202 

1711.1 

1.6 

1946 

16.02 

18.62 

352  41  59.91 

2811 

9951 

1098 

5109.1 

1.3 

1947 

16.07 

18.73 

58.09 

2810 

9974 

0994 

5474.1 

1.1 

1948#. 

16.12 

18.84 

56.26 

2809 

!l.959i)ii!ii; 

6899 

5s  10.  1 

1.9 

1949 

89  58  16.18 

1  27  18.95 

352  41  54.46 

9.9992M19 

9.9600018 

9.61707  s<; 

6205.1         1.6 

earli  of  the  quantities  K',,  AT,  and  k,,  l\\<-  rmigtant  U0".00  has  been  subtracted;  and  from  log  ky  tlic  coiistaiii 

and  from  log  A,  the  cnn.staiit  0.00005CO. 
15  V 


TABLE  XL,. 


Corrections  of  K^  7fv,  ($-r.,  ilur  lo  Lunar  Nutation,  for  1850. 

Period  of  Argument  XV.,  iiTilt-'i.'J. 

Arg- 
XV. 

A  A*. 

A  Ay. 

A  A;. 

V;ir.  in    ,   ,       , 
100  yrs.  Alogiy.Alog.iz 

Are. 
XV. 

A  K*. 

A  Ay.   A  A',, 

V:ir.  ill   , 

lOOyre.  Al°s/*> 

Alog.i,. 

d 

// 

// 

-/, 

// 

a    // 

//      // 

// 

0 

18.00 

18.63 

20.05 

+0.03 

1 

850 

2400  32.02 

81.70 

28.47 

-0.02 

148 

140 

50 

18.78 

19.42 

20.79 

0.03 

1 

847 

2450  31.53 

31.18 

27.89 

0.02 

151 

125 

100 

19.56 

20.20 

21.52 

0.03 

2 

844 

2500  31.00 

30.63 

27.28 

0.02 

154 

111 

150 

20.34 

20.98 

22.25 

0.03 

3 

840 

2550  30.45  30.05 

26.64 

0.02 

157 

98 

200 

21.11 

21.75 

22.95 

0.03 

4 

835 

2600 

29.87 

29.45 

25.99 

0.03 

160 

86 

250 

21.87 

22.50 

23.65 

+0.02 

5 

829 

2650 

29.26 

28.82 

25.32 

-0.03 

162 

74 

300 

22.63 

23.25 

24.33 

0.02 

7 

822 

2700  28.63  ' 

28.17 

24.63 

0.03 

164 

63 

850 

23.38 

24.00 

25.00 

0.02 

8 

814 

2750  27.97 

27,19 

23.92 

0.03 

166 

53 

400 

24.12 

21.71 

25.66 

0.02 

10 

806 

2800  27.29 

26.78  23.19 

0.03 

168 

44 

450 

24.85 

25.46 

96.30 

0.02 

12 

797 

2850 

26.59 

26.06 

22.45 

0.03 

170 

36 

500 

25.57 

26.17 

26.93 

+0.02 

14 

787 

2900 

25.87 

25.33 

21.70 

-0.03 

172 

28 

550 

26.27 

26.86 

27.53 

0.02 

16 

777 

2950  ;  25.13  24.58 

20.94 

0.03 

173 

21 

GOO 

26.94 

27.52 

28.10 

0.02 

19 

766 

3000 

24.38  23.81 

20.17 

0.03 

174 

16 

650 

27.60 

28.17 

28.65 

0.02 

21 

754 

3050 

23.61 

23.03 

19.39 

0.03 

175 

11 

700 

28.25 

28.80 

29.19 

0.02 

24 

741 

3100 

22.83 

22.23 

18.60 

0.03 

176 

7 

750 

28.87 

29.41 

29.69 

+0.02 

27 

727 

3150 

22.04 

21.43 

17.81 

-0.03 

176 

4 

800 

29.47 

29.99 

30.17 

0.02 

29 

713 

3200 

21.24 

20.62 

17.02 

0.03 

177 

2 

850 

30.05 

30.55 

30.62 

0.01 

32 

699 

3250 

20.43 

19.80 

16.23 

0.03 

177 

1 

900 

30.60 

31.09 

31.05 

0.01 

36 

684 

3300 

19.62 

18.99 

15.45 

0.03 

177 

0 

950 

31.13 

31.60 

31.45 

0.01 

39 

668 

3350 

18.80 

18.16 

14.66 

0.03 

177 

1 

1000 

31.63 

32.08 

31.81 

+0.01 

42 

652 

3400 

17.98 

17.34 

13.88 

-0.03 

177 

3 

1050 

32.10 

32.53 

32.14 

0.01 

46 

635 

3450 

17.16 

16.51 

13.10 

0.03 

176 

5 

1100 

32.55 

32.95 

32.45 

0.01 

49 

618 

3500 

16.35 

15.70 

12.31 

0.03 

175 

9 

1150 

32.97 

33.34 

32.73 

0.01 

53 

600 

3550 

15.54 

14.89 

11.59 

0.03 

174 

13 

1200 

33.35 

33.70 

32.97 

+0.01 

57 

582 

3600 

14.73 

14.09 

10.84 

0.03 

173 

18 

1250 

33.70 

34.03 

33.18 

0.00 

61 

564 

3650 

13.93 

13.29 

10.11 

-0.03 

172 

24 

1300 

34.02 

34.32 

33.35 

0.00 

64 

545 

3700 

13.14 

12.50 

9.40 

0.02 

171 

31 

1350 

34.31 

34.58 

33.  19 

0.00 

68 

526 

3750 

12.36 

11.72 

8.70 

0.02 

169 

39 

1400 

34.56 

34.81 

33.60 

0.00 

72 

507 

3800 

11.59 

10.96 

8.02 

0.02 

167 

48 

1450 

34.78 

35.00 

33.67 

0.00 

76 

488 

3850 

10.84 

10.22 

7.36 

0.02 

165 

58 

1500 

34.96 

35.16 

33.70 

0.00 

80 

469 

3900 

10.10 

9.49 

6.72 

-0.02 

163 

68 

1550 

35.10 

35.27 

33.70 

0.00 

84 

449 

3950 

9.38 

8.78 

6.11 

0.02 

160 

80 

1600 

35.21 

35.35 

33.66 

0.00 

88 

429 

4000 

8.68 

8.10 

5.52 

0.02 

158 

92 

1G50 

35.28 

35.39 

33.58 

-0.01 

93 

410 

4050 

8.00 

7.43 

4.95 

0.02 

155 

104 

1700 

35.32 

35.40 

33.48 

0.01 

97 

390 

4100 

7.35 

6.79 

4.42 

0.02 

152 

118 

1750 

35.32 

35.37 

33.34 

-0.01 

101 

370 

4150 

6.72 

6.18 

3.91 

-0.02 

150 

132 

1800 

35.29 

35.31 

33.17 

0.01 

105 

351 

4200 

6.11 

5.59 

3.43 

0.02 

146 

146 

1850 

35.21 

35.20 

32.96 

0.01 

109 

332 

4250 

5.53 

5.02 

2.98 

0.01 

143 

162 

1900 

35.10 

35.06 

32.71 

0.01 

113 

313 

4300 

4.98 

4.49 

2.56 

0.01 

140 

178 

1950 

34.95 

34.88 

32.42 

0.01 

117 

294 

4350 

4.46 

3.99 

2.18 

0.01 

137 

194 

2000 

34.77 

34.67 

32.11 

-0.01 

120 

275 

4400 

3.96 

3.52 

1.82 

-0.01 

133 

211 

2050 

34.55 

34.42 

31.76 

0.02 

124 

257 

4450 

3.50 

3.08 

1.50 

0.01 

129 

22!) 

2100 

34.29 

34.14 

31.3S 

0.02 

128 

239 

4500 

3.07 

2.67 

1.21 

0.01 

126 

247 

2150 

34.00 

33.82 

30.97 

0.02 

132 

221 

4550 

2.68 

2.30 

0.97 

0.01 

122 

265 

2200 

33.67 

33.46 

30.53 

0.02 

135 

204 

4600 

2.32 

1.97 

0.75 

-0.01 

118 

284 

2250 

33.31 

33.07 

30.06 

-0.02 

139 

187 

4650 

1.99 

1.67 

0.57 

0.00 

114 

303 

2300 

32.91 

32.64 

29.55 

0.02 

142 

171 

4700 

1.70 

1.40 

0.43 

0.00 

110 

322 

2350 

32,18 

32.18 

29.02 

0.02 

145 

155 

4750 

1,44 

1.17 

0.32 

0.00 

106 

841 

2400 

32.02 

31.70 

28.47 

-0.02 

148 

140 

4800 

1.22 

0.98 

0.25 

0.00 

102 

360 

A  log  ky  al><l  A  log  /':/.  i'f"  ill  units  of  till!  suvuiitli  ilcriinal  place. 

The  constants  added  arc,  1H".00  to  A  A"s,  J8".()0  to  A  A'y,  ]  7"-0()  to  A  A",.,  ^  t<>  A  log  l;y,  and  430  to  A  log  kz. 

TABLE  XL 


TABLE  XL.I. 


Cum                                                         '  unnr  .\utalinn,  / 

•/•  .\ntnlitin,  fur  1 

IVrioil  ufArsum.'iit  XV.,  1 

,   m  \  VI  .  966  '-'I 

ArS. 
XV. 

AAV 

AAV 

Var.in 
IDOyn. 

log*, 

\\  1 

AAV 

AAV 

AAV 

Vnr.  ill 

lililyrs. 

Al»g*y 

.I,,./., 

BolM 

iNilIal'll 

ll 

// 

// 

n 

// 

.1 

II 

// 

// 

n 

// 

4800 

1.22 

0.25 

().()() 

102 

0 

2.36 

2.33 

3-17 

0.00 

6 

105 

+0.3(i 

1850 

1.04 

0.83 

0.22 

().()() 

98 

880 

5 

2.57 

2.5  1 

3.36 

0.00 

(i 

105 

0.57 

4900 

0.89 

0.71 

0.22 

o.oo 

94 

100 

10 

2.7(1 

2.7  I 

8.53 

0.00 

6 

106 

0.76 

4950 

0.78 

0.68 

0.25 

0.00 

90 

120 

15 

2.92 

2.9  1 

3.6N 

0.00 

(i 

107 

0.92 

0.71 

0.58 

0.83 

+0.01 

Mi 

139 

20 

3.06 

8.05 

3.81 

0.00 

5 

109 

1.06 

5050 

0.68 

0.58 

0.11 

+0.01 

81 

159 

25 

8.16 

8.16 

8.91 

0.00 

5 

111 

+  1.16 

5100 

0.68 

0.61 

0.01 

T1) 

479 

30 

3.22 

3.23 

3.9N 

0.00 

4 

114 

1.22 

5150 

0.72 

0.68 

0.76 

0.01 

73 

498 

85 

3.25 

3.26 

1.01 

0.00 

1 

117 

1  .25 

5200 

0.79 

0.7s 

0.91 

0.01 

69 

:.  i  ; 

40 

3  25 

8.26 

101 

40.01 

3 

120 

1.21 

5250 

0.90 

0.92 

1.2'J 

0.01 

lit; 

586 

(5 

3.20 

3.22 

8.97 

0.01 

2 

123 

1.19 

5300 

.().-, 

1.10 

1.50 

+0.01 

62 

">5.") 

50 

3.  1  1 

3.11 

3.89 

+0.01 

2 

126 

+  1.10 

5350 

.23 

1  .3  1 

1.81 

0.01 

55 

3.02 

3.77 

0.01 

1 

128 

0.98 

5  100 

.45 

1.56 

2.  1  .'. 

0.02 

54 

60 

2.8  1 

3.63 

0.01 

1 

131 

0.88 

5  1:.0 

.70 

1.84 

2.52 

0.09 

50 

609 

65 

2.66 

2.7  1 

3.46 

0.01 

1 

132 

0.65 

5500 

.99 

2.16 

2.93 

0.02 

47 

627 

70 

2.  17 

2.52 

3.26 

0.01 

0 

133 

0.46 

5550 

2.31 

2.51 

3.36 

+0.02 

13 

(ill 

7.') 

2.26 

2.31 

3.0  1 

+0.01 

0 

133 

+0.25 

5600 

2.67 

2.89 

0.02 

40 

660 

80 

2.05 

2.10 

2.82 

0.01 

0 

133 

*(>.OI 

5650 

3.06 

8.3] 

•1.33 

0.02 

37 

676 

85 

1.83 

1.88 

2.59 

0.01 

1 

132 

-0.18 

5700 

3.  17 

8.75 

I.M 

0.02 

33 

692 

90 

1.62 

1.67 

2.35 

0.01 

1 

130 

0.39 

5750 

8.91 

L22 

5.37 

0.02 

30 

707 

05 

1.12 

1.47 

2.12 

0.01 

2 

127 

0.59 

5800 

L39 

4.72 

5.98 

+0.02 

27 

721 

100 

1.21 

1.29 

1.91 

+0.01 

2 

121 

-0.77 

5850 

L89 

5.2  1 

6.52 

0.02 

21 

735 

105 

1.01) 

1.13 

.72 

0.01 

3 

120 

0.92 

5900 

5.  12 

5.80 

7.18 

0.02 

22 

'  is 

110 

0.97 

1.00 

.55 

0.0  1 

4 

115 

1.05 

5950 

5.9* 

6.38 

7.76 

0.02 

19 

760 

115 

0.87 

0.90 

.10 

0.02 

5 

110 

1.15 

6000 

6.56 

6.98 

8.11 

0.03 

17 

772 

120 

0.81 

0.83 

.29 

0.02 

6 

lor, 

1.21 

6050 

7.16 

7.60 

9.07 

+0.03 

14 

783 

125 

0.78 

0.80 

.20 

+0.02 

'     8 

99 

-1.24 

6100 

7.78 

S.2  I 

9.74 

0.03 

12 

793 

130 

0.78 

0.80 

.15 

0.02 

9 

91 

1.21 

6150 

N.  12 

8.90 

10.13 

0.03 

10 

803 

135 

0.82 

0.83 

.13 

0.02 

10 

88 

1.20 

6200 

9.09 

9.59 

11.11 

0.03 

9 

811 

110 

O.S9 

0.90 

.14 

0.02 

11 

N;{ 

1.13 

6250 

9.77 

10.89 

11.86 

0.03 

7 

819 

115 

1.00 

1.00 

.19 

0.02 

12 

77 

1.02 

6800 

10,17 

11.01 

12.59 

+0.03 

6 

826 

150 

1.13 

1.13 

.27 

+0.02 

13 

72 

-6.89 

6350 

11.18 

11.73 

13.32 

0.03 

4 

832 

155 

1.29 

1  .29 

.88 

0.02 

11 

68 

0.73 

6400 

11.91 

12.47 

1  1.07 

0.03 

3 

838 

160 

1,17 

1.17 

.51 

0.02 

15 

til 

0.55 

6  150 

12.65 

13.23 

1  1.N2 

0.03 

Q 

842 

165 

1.67 

1.67 

.66 

0.02 

16 

60 

0.35 

6500 

13.  10 

13.99 

15.57 

0.03 

2 

846 

170 

1.87 

1.87 

.89 

0.02 

16 

58 

-0.15 

6550 

11.  1C 

14.76 

10.33 

+0.03 

1 

848 

176 

2.08 

2.0s 

1.99 

+0.02 

17 

56 

+0.06 

6600 

1  !.!)-,> 

15.53    17.08 

0.03 

1 

850 

180 

2.28 

2J28 

2.16 

0.02 

17 

54 

0.26 

6650 

15.69 

l(i.31     17.  S3 

0.03 

0 

851 

IK.') 

2.  is 

2.  1!) 

2.33 

0.03 

17 

r.l 

0.46 

6700 

16,17 

17.0!)    18.58 

0.03 

0 

852 

190 

2.67 

2.  (IS 

2.  19 

0.03 

17 

51 

0.64 

6750 

17.25 

17.88 

19.33 

0.03 

1 

851 

195 

2.84 

2.85 

2.6  1 

0.03 

16 

56 

0.81 

6800 

1  8.0:5 

18.66 

20.0S 

+0.03 

1 

849 

200 

2.99 

3.01 

2.78 

.0.03 

16 

56 

+  0.96 

685D 

18.81 

19.  15   20.82 

0.03 

1 

847 

205 

3.11 

3.11 

2.89 

0.03 

16 

57 

1  .08 

6900 

19.59 

20.23 

21.55 

0.03 

2 

Ml 

210 

3.19 

8.23 

2.91 

0.03 

16 

60 

1.16 

6950 

20.37 

21.01 

22.27 

0.03 

3 

840 

215 

3.25 

3.29 

3.03 

0.03 

15 

62 

1.22 

7000 

21.11 

81.78 

22.!  is 

0.03 

4 

N35 

290 

3.27 

8.39 

8.06 

0.03 

15 

65 

1.21 

7050 

21.90 

22.5  1 

23.68 

+0.02 

:. 

829 

225 

8.26 

3.32 

3.05 

+0.03 

14 

68 

+  1.23 

7100 

22.66 

23.29 

2J.36 

0.02 

7 

822 

230 

3.22 

3.29 

3.02 

0.03 

ll 

71 

1.19 

7150 

23.  :  i 

2  1.03 

25.03 

0.02 

s 

Nil 

235 

3.11 

3.22 

2.95 

0.03 

13 

73 

1.11 

7200 

22.  1  1 

24.76 

25.68 

+0.02 

10 

806 

2  10 

8.09 

3.11 

2.  si 

+0.03 

13 

76 

+  1.00 

A  l«>g  '•">•  n  ml  /'    •                                                          '  'li'i-imal. 
TABLE  XI.  1.—  r..nstants  ad.l.'.l  «re,  -J'Mi  i  L.  A  K*,  S'MKI  to  A  ATy,  3'                                                              0  to  A  log  t. 

TABL.E  XL.I. 


TABLE  XL1II. 


('  rri'ctions  of  K*,  Ky,  4"f-i  lluc  l"  Solar  Nutation,  for  1850. 

Parcillti.r  end  Semi-diameter. 

Period  of  Argument  ,\VI..  3G.j<1.'.>4. 

Arg. 
XVI. 

A  Kx. 

A    Ky. 

A  K,, 

Var.  in 
lOOyrs. 

A.og,y. 

A'og/.-,, 

Solar 
Niitat'n 

Log. 
diet.  from 

Parallax 

Semi- 
diam. 

Log. 

ditit.from 

i 

Parallax 

Semi- 
(liam. 

fl 

11 

to 

n 

n 

Earth. 

Earth. 

9,lfl 

Q 

A'! 

Q    1  1 

2.84 

+0.03 

13 

76 

+1.00 

^  iw 

2  15 
250 
255 
260 

«L>    \J*J 

2.89 
2.72 
2.5  1 
2.35 

f  J.  1  A 

2.97 
2.S1 
'2.63 
2.44 

2.71 
2.54 
2.36 
2.16 

0.03 
0.03 
0.08 
0.04 

12 
12 
12 
12 

78 
79 
80 
81 

0.86 
0.69 
0.51 
0.31 

9.40 
9.41 
9.42 
9.43 

35.22 
34.42 

38.6  1 

32.87 

31.02 
33.25 
32,19 
31.75 

9.85 

9.86 

9.87 
9.88 

12'.50 
12.21 
11.94 
11.66 

ii 

12.07 
11.80 
11.53 
11.27 

205 

2 

11 

2.23 

1.93 

+0.04 

12 

81 

+0.10 

9.44 

32.13 

81.03 

9.89 

11.40 

11.01 

270 

1 

92 

2.01 

1.70 

0.01 

12 

80 

-0.12 

275 

1 

71 

1.80 

1.47 

0.04 

12 

78 

0.33 

9,45 

81.39 

30.32 

9.90 

11.14 

10.76 

2SO 

1 

51 

1.60 

1.24 

0.04 

13 

76 

0.53 

9.46 

30.68 

29.63 

9.91 

10.89 

10.51 

285 

1 

82 

1.41 

1.02 

0.04 

13 

72 

0.72 

9.47 

29.98 

28.96 

9.92 

10.64 

10.27 

290 

29.0 

1 
1 

15 

00 

1.23 
1.08 

0.81 
0.62 

+0.04 
0.04 

14 
15 

69 
64 

-0.89 
1.04 

9.48 
9.49 

29.30 
28.63 

28.30 
27.65 

9.93 
9.94 

10.40 
10.16 

10.04 
9.81 

300 
805 
310 

0.89 
O.S2 

0.78 

0.96 
0.88 
0.84 

0.46 
0.34 
0.25 

0.01 
0.04 
0.04 

16 
17 

19 

59 
54 

48 

1.15 
1.22 
1.26 

9.50 
9.51 
9.52 

27.98 
27.34 
26.72 

27.02 
26-40 
25.81 

9.95 
9.96 
9.97 

9.93 
9.70 

9.48 

9.59 
9.87 
9.16 

815 

0 

79 

0.84 

0.20 

+0.04 

20 

42 

-1.25 

9.53 

26.11 

25.22 

9.98 

9.26 

8.95 

820 

0 

0.18 

0.04 

21 

36 

1.21 

9.54 

25.52 

24.65 

9.99 

9.05 

8.74 

825 

0 

Dl 

Q.i  6 

0.20 

0.04 

22 

31 

1.13 

330 

1 

02 

1.07 

0.25 

0.04 

23 

25 

1.02 

9.55 

24.94 

24.09 

0.00 

8.85 

8.55 

8:35 

1 

17 

1.20 

0.33 

0.05 

24 

20 

0.88 

9.56 

21.37 

23.51 

0.01 

8.65 

8.35 

310 
8  15 
350 

1 

1 
1 

33 
51 
72 

1.36 
1.54 
1.75 

0.44 
0.57 
0.73 

+0.05 
0.05 
0.05 

25 
26 

27 

15 
11 

8 

-0.72 
0.54 
0.33 

9.57 
9.58 
9.59 

23.81 
23.27 
22.74 

23.00 

22.48 
21.97 

0.02 
0.03 
0.04 

8.45 
8.26 
8.07 

8.16 
7.98 
7.79 

855 
360 

1 

2 

95 

18 

1.98 
2.22 

0.92 
1.11 

0.05 
0.05 

27 
28 

5 
3 

-0.10 
+0.13 

9.60 
9.61 

22.23 

21.72 

21.47 

20.98 

0.05 
0.06 

7.89 
7.71 

7.62 
7.44 

365 

2 

40 

2.44 

1.30 

+0.05 

28 

2 

+0.35 

9.62 

21.22 

20.50 

0.07 

7.53 

7.27 

870 

2 

61 

2.65 

1.49 

+0.05 

28 

2 

+0.56 

9.63 

20.74 

20.03 

0.08 

7.36 

7.11 

9.64 

20.27 

19.58 

0.09 

7.19 

6.95 

A  lo"  li,  and  A  log  ^z  are  'n  »"''*  of  the  seventh  decimal. 

Constants  added  are,  2'_'.0<ho  A  K*,2".(M  to  A  Ky,  3".00  to  A  Kz, 

9.65 

19.81 

19.13 

0.10 

7.03 

6.79 

1  to  A  log  fcy,  antl   IM  to  A  log  Kz. 

9.66 

19.36 

18.70 

0.11 

6.87 

6.63 

TABLE  XLII. 

9.67 
9.68 

18.92 

18.49 

18.27 
17.85 

0.12 
0.13 

6.71 
6.56 

6,18 
6.81 

Factors  for  obtaining  A  x,  A  y,  A  z/rom  A  /?•     . 

9.69 

18.07 

17.45 

0.14 

6.41 

6.19 

Orbit. 

Long. 

For  A  z- 

For  A  y- 

For  A  z. 

9.70 

17.65 

17.05 

0.15 

6.26 

6.05 

9.71 

17.25 

16.66 

0.16 

6.12 

5.91 

o 

9.72 

16.86 

16.28 

0.17 

5.98 

5.78 

6 

180 

+  0-020 

-0.145 

+  0.322 

9.73 

16.48 

15.91 

0.18 

5.85 

5.65 

10 

190 

0.018 

0.148 

0.323 

9.74 

16.10 

15.55 

0.19 

5.71 

5.52 

20 

200 

0.016 

0.150 

0.324 

30 

210 

0.013 

0.152 

0.325 

9.75 

15.73 

15.20 

0.20 

5.58 

5.39 

40 

220 

0.009 

0.152 

0.325 

9.76 

15.38 

14.85 

0.21 

5.46 

5.27  - 

50 

230 

+  0.006 

-0.151 

+  0.325 

9.77 

15.03 

14.51 

0.22 

5.33 

5.15 

60 

240 

0.003 

1  0.149 

0.324 

9.78 

14.68 

14.18 

0.23 

5.21 

5.03 

70 

250 

0.001 

0.146 

0.823 

9.79 

14.35 

18.86 

0.24 

5.09 

4.92 

80 

260 

0.000 

0.143 

0.821 

90 

270 

0.000 

0.139 

0.320 

9.80 

14.02 

13.54 

0.25 

4.98 

4.81 

9.81 

13.70 

13.24 

0.26 

4.86 

4.70 

100 

280 

+  0.002 

-0.136 

+  0.319 

9.82 

13.39 

12.93 

0.27 

4.75 

4.59 

110 

290 

0.004 

0.134 

0.318 

9.83 

13.09 

12.64 

0.28 

4.64 

4.48 

120 

300 

0.007 

0.132 

0.317 

9.84 

12.79 

12.35 

0.29 

4.54 

4.38 

130 

310 

0.011 

0.132 

0.317 

9.85 

12.50 

12.07 

0.30 

4.43 

4.28 

140 

320 

0.014 

0.133 

0.317 

150 

330 

+  0.017 

-0.135 

-1-0.318 

160 

340 

0.019 

0.138 

0.319 

170 

850 

0.020 

0.141 

0.321 

180 

360 

+  0.020 

-0.145 

+  0.322 

TAHL.13   XL.IV. 


Mt'fittn   of  tin'    Argument*  for   O/////r/V.s\ 

Century. 

<< 

/'  -  50, 

111 

I. 

I'  _.-,:!. 

II. 

III. 

IV. 

V. 

VI 

VII. 

\  III 

O          /          // 

II 

d 

d 

y 

.1 

d 

d 

d 

d 

it 

-300 

i.v,  .-,:,    .-.oo 

-0.1763 

-3111 

11  5.!)!  151 

-0.000514 

50.: 

!        171 

2381 

1103.1 

359.68 

172.2 

116.5 

-2(KI 

:{.-,:>    7    3.60 

0.4536 

3251 

14.7184 

0.000100 

150.: 

{        731 

437 

13  11.7 

581.51 

•2-2-2.  1 

27.5 

-100 

101    10      Mil 

O.I300 

3089 

138.1447 

0.000165 

II. 

1207 

1451 

II.  1 

310.51 

•20,-. 

150.1 

0 

33  :!l      I.NI 

0.4082 

2020 

36.8726 

0.1)001  II 

111. 

1061 

2166 

103.0 

57,1( 

70.S 

70.1 

100 

232    13      l.:r. 

03856 

2761 

1  60.30:  W 

0.000116 

211. 

2121 

521 

311.6 

370.31 

130.1 

201.6 

200 

71   55     0.11 

-03639 

-2601 

50.0366 

-0.000302 

72.  1 

1535 

106.2 

117.20 

ISO.:) 

112.6 

300 

271     7    16.14 

0.3102 

8439 

1-2.1726 

0.000367 

172,1 

3550 

2550 

6I7.S 

430.17 

230.6 

23.6 

K 

100 

III)    10  25.13 

0.3175 

2276 

SI.  2  103 

0.0003  13 

33.5 

4111 

605 

700.1 

i;;.  2 

37.7 

155.2 

d 

500 

300  31   3ti 

0.2:  'is 

3114 

201.6513 

0.0003  IS 

133.5 

1677 

1620 

951.0 

400.00 

--.o 

6i;.2 

a  t 

(WO 

148  43  50.82 

0.2722 

1851 

103.3030 

0.000-201 

2:i3.5 

5210 

3634 

1102.6 

236.05 

l:!S.:{ 

187.8 

L. 

c 
- 

700 

347  50    6.1  r> 

-0.210.-, 

-1788 

2.1389 

-0.000269 

94.0 

5809 

no 

12.-,  1.2 

558.83 

I--.:, 

•3 

soo 

1-7      S  -.'5.20 

0.2268 

1626 

I25.5S72 

0.0002  15 

lOl.t 

6:  )67 

1704 

1  I05.S 

200.78 

23S.S 

IO.S 

•^ 

000 

26  20    I.--.02 

0.2011 

1463 

21.3372 

0.000-220 

55.7 

6!  130 

27  is 

102.5 

31.73 

45.0 

151.3 

225  33 

0.1814 

1301 

117.7003 

0.000  l!Mi 

155.7 

7403 

771 

854.1 

356.1  il 

!Ni.2 

62,3 

1100 

61   45  33.00 

0.1586 

1  i:(S 

4  6.5  152 

0.000171 

16.S 

8056 

1788 

405.7 

94.56 

116.1 

103.0 

1200 

203  58      1.13 

-0.1361 

-  076 

170.0033 

-0.000  1  17 

110.8 

2803 

557.3 

116.11 

106.7 

101.0 

131X1 

103   10  31.1  1 

O.I  131 

813 

08.7030 

0600189 

2I6.S 

9183 

858 

70S.ii 

154.30 

3.H 

15.0 

1400 

30-2  23     :!.!! 

0.0007 

651 

102.2200 

0.0000!  »8 

77.8 

0716 

IS72 

860.5 

476.20 

51.1 

147.4 

1500 

141  :{.-.  3; 

0.0680 

488 

90.0006 

0.000073 

177.8 

10300 

2887 

1012.1 

211.22 

104.4 

•>.l 

S    1500 

125  31    I0.2S 

-0.0680 

.    1" 

8<).!>900 

-0.000073 

177.8 

10-200 

2877 

1002.1 

204.22 

01.  1 

1     1600 

:{•.'!    Hi  55.70 

0.0454 

326 

204.4585 

0.000010 

3S.O 

10863 

032 

lisa? 

526.00 

11  1.6 

' 

—     1/vO 

162  23  26.76 

-0.0227 

-   163 

102.2280 

-0.000024 

13S.O 

1  1425 

1016 

1301.3 

263.05 

103.0 

90.'  1 

C     : 

000 

0 

0.0000 

0.000000 

0.0 

0 

0 

0.0 

0.00 

0.0 

C..I 

a 

a 

1000 

107  36  35.51 

+0.0-227 

+   162 

1-22.4752 

+0.000024 

100.0 

502 

1013 

150.6 

320.88 

10.3 

130.6 

o 
jc 

2000 

36  40  21.09 

0.0454 

335 

21.2521 

0.000040 

200.0 

1125 

8688 

302.2 

5s.s:l 

ilO.5 

41.6 

£ 

2100 

234  26     1.13 

40.0680 

+  487 

1  13.73-2-2 

+0.000073 

61.1 

I6SS 

89 

I52.S 

370.70 

1  l-.s 

172.1 

(9 

,2200 

72     2  43.41 

+0.0007 

+  650 

41.5140 

+0.000098 

101.1 

2250 

1090 

603.4 

116.116 

198.1 

S2.  1 

Century 

IX. 

X. 

XI. 

XII. 

XIII. 

XIV. 

log  sin  t. 

t'  —  50. 

363°  -Q. 

«'  —  50. 

XV. 

\V1 

-300 

129*81 

35.01 

1S0.76 

10.0 

56.38 

25.2 

-0.0031028 

+21.61 

0           i           11 

+18  46  55.6 

+<>.'63I 

1190*0 

d 

-1.4 

-200 

15S.06 

56.10 

t  J."'.~i      ^IS.S 

23.00 

3.8 

0.00294$! 

23.11 

17  53  46.0 

0.601 

3721.3 

3.6 

-100 

18630 

44.00 

165.31 

3S.1 

47.71 

17.0 

0.0027850 

22.27 

17     0  33.4 

0.574 

625S.O 

2.H 

0 

211.:,.-, 

5.25 

831.40 

57.0 

11.03 

32.1 

0.0020270 

21.10 

Hi     7   I7.S 

0.544 

1003.4 

2.1 

100 

5.80 

53.15 

149.80 

56.3 

39.04 

93 

0.0024719 

10.92 

15  13  50.1 

0.513 

1527.1 

1.3 

200 

34.05 

14.30 

215.05 

15.1 

6.26 

24.5 

-0.0023171 

+1S.75 

+14  20  37.4 

+O.I.-3 

262,-. 

-0.5 

300 

62.30 

2.20 

134.41 

14.4 

30.37 

2.3 

0.002  K  !35 

17.58 

13  27  12.7 

0.453 

2700.2 

+0.3 

fe 

400 

90.54 

200.50 

33.3 

57.50 

10.S 

0.0020111 

16.11 

12  :{:{  45.0 

0.423 

5329.9 

1.1 

c 

500 

II  -.7:1 

1  l.-'li 

118.00 

32.6 

21.70 

30.0 

0.0018508 

15.24 

11  40  1  1.3 

0.303 

1065.3 

L8 

B 
-  , 

000 

147.03 

32!l  1 

1S5.05 

51.4 

48.92 

93 

0.0017097 

14.00 

10  40  40.0 

0.362 

35!  10.0 

2.6 

C 

700 

175.28 

53.57 

11.15 

10.3 

16.14 

23.7 

-0.0015008 

+12.89 

+  0  53    3.8 

+0.332 

6132.7 

+3.1 

IS 

800 

203.53 

41,17 

16;  1.60        9.0 

10.2.-, 

1.5 

0.0014130 

11.72 

S  50  21.0 

0309 

1868.1 

1.2 

* 

000 

231.77 

2.62 

235.70     28.5 

7.47 

16.1 

0.0012665 

10.55 

8    5  41.2 

0.272 

4401.8 

."..I) 

1000 

23.03 

5052 

151.15 

27.8 

31.57 

29.9 

0.0011211 

938 

7  11  55.4 

0.212 

137.3 

.">.- 

1100 

51.27 

11.68 

220.25 

40.0 

58.79 

8.4 

0.000076- 

8.20 

0   18     0.5 

0.211 

2071.0 

6.5 

1200 

79.52 

59.58 

138.70 

45.9 

22.90 

22.2 

-0.0008338 

+  7.03 

+  5  24  14.0 

+0.181 

5204.0 

+7.3 

1300 

107.70 

20.73 

204.SO 

4.8 

50.12 

0.8 

0.0000010 

5.80 

4  30   10.7 

0.151 

010.1 

S.I 

1400 

136.01 

8.63 

123.25 

4.1 

1  1.23 

14.6 

0.000.-,.-,  12 

4.(iO 

3  36  21.8 

0.121 

3173.x 

S.ll 

J500 

161.25 

29.79 

189.35 

23.0 

41.45 

29.1 

0.0004110 

3.52 

2  42  20.0 

0.0!)  1 

0007.5 

+9.7 

ij 

1500 

154.25 

29.79 

180.35 

23.0 

41.45 

29.1 

-0.0004116 

+  3.52 

+  2  42  20.0 

+0.001 

5007.5 

-0.3 

fl 

I6IUI 

1.  -2.50 

17.60 

I07.SO 

22.2 

-,  ;,  ; 

6.9 

0.0002732 

2.31 

1  48  17.0 

0.060 

17:  f2.!» 

40.1 

• 

1700 

209.75 

173.00 

II.  1 

33.78 

21.4 

-0.000  1  3!  k) 

+  1.17 

+  o  :>l  10.0 

+0.030 

4205.6 

+0.2 

cS 

1800 

0.00 

'o!oo 

0.00 

0.0 

0.00 

0.0 

0.0000000 

0.00 

0    0    0.0 

0.000 

0.0 

0.0 

c  • 
.2 

1000 

27.25 

47.00 

158,15 

:,'•; 

24.11 

13.8 

+0.0001310 

-  1.17 

-  0  51  13.0 

-0.030 

2532.7 

-0.2 

c 
•B 

2000 

55.49 

0.05 

22l,->5 

18/2 

5133 

883 

0.00026-5 

2.34 

1  48  20.0       0.060 

5000.1 

+0.0 

2100 

82.74 

56.!  15 

113.00 

17.1 

15.11 

ai 

0.000401  1 

3.52 

2    12    Kl        0.001 

0.3 

0 

2200 

109.98 

18.11 

36.3 

12.68 

' 

20.7 

+0.0005324 

-    1.6.1 

-  3  37    10.2      -0.121 

1 

.•{.•ecu 

+0.1 

8O 


TABLE   XL.VI. 


TAIIL1J   XI.V. 

Reduction  to  the  Ecliptic  for  1850. 

Values  of  /he  Equation 

Argument  =  Orbit  Longitude  -f-  (360°  —  Q),  or  this  angle  diminished  by  180°. 

+  147°.!.) 

Arg. 

0' 

10' 

20' 

30' 

40' 

5O' 

Diff. 

for  10 

Var.  in 
100  yrs. 

Equa. 

Din",  for 

o 

/      // 

H 

n 

u 

ii 

n 

n 

n 

o 

Year. 

III  yrs. 

0 

-0    0.00 

1.05 

2.10 

3.15 

4.21 

5.26 

1.05 

0.00 

179' 

1 

0     6.31 

7.36 

8  41 

i)  ||j 

10  ril 

H<)6 

1  O^i 

o  on 

17SJ 

/, 

2 

0  12.61 

13.66 

O.T:  1 

14.71 

15.76 

J.\/.iJ  1 

16.80 

,*J\J 

17.85 

1.05 

\j  \\j\j 

-0.01 

J.  <O 

177 

1800 

H 

-0.281 

-   3 

3 

0  18.90 

19.94 

20.99 

22.04 

23.08 

24.12 

1.05 

0.01 

176 

1810 
1820 

0.251 

15 

27 

4 

0  25.16 

26.20 

27.24 

28.28 

29.31 

30.35 

1.04 

0.02 

175 

1830 

0.218 

37 

5 

-0  31.39 

32.43 

33.46 

31.50 

35.53 

36.56 

1.03 

-0.02 

174 

1840 

0.176 

45 

6 

0  37.59 

38.61 

39.64 

40.66 

41.69 

42.71 

1.09 

0.02 

173 

7 

0  43.71 

44.76 

45.77 

46.79 

47.80 

48.82 

1.01 

0.03 

172 

1850 

+U.12H 

-51 

8 

0  49.83 

50.84 

51.85 

52.85 

53.86 

54.87 

1.01 

0.03 

171 

1860 
1870 

0.073 
+0.016 

66 

58 

9 

0  55.87 

56.87 

57.86 

58.86 

59.85 

60-85 

1.00 

0.03 

170 

1880 

-0.043 

58 

10 

-1     1.84 

2.83 

3.82 

4.80 

5.78 

6.76 

0.98 

-0.04 

169 

1890 

U.1UU 

54 

11 

1     7.73 

8.71 

9.68 

10.65 

11.62 

12.58 

0.97 

0.04 

168 

1900 

-0.152 

-49 

12 
13 

1   13.54 

1   19.26 

14.50 
20.20 

15.46 
21.14 

16!  41 
22.08 

17.36 
23.01 

18.31 
23.95 

0.95 

0.94 

0.05 
0.05 

167 
166 

1910 

42 

14 

1  24.88 

25.81 

26.74 

27.66 

28.58 

29.50 

0.92 

0.05 

165 

1920 

0.236 

31 

1930 

0.261 

20 

15 

-1  30.41 

31.32 

32.23 

33.13 

34.03 

31.93 

0.90 

-0.06 

164 

1940 

0.277 

-10 

16 

1  35.82 

36.71 

37.60 

38.48 

39.36 

40.24 

0.88 

0.06 

163 

1950 

-0.282 

+  2 

17 

18 

1  41.11 
1  46.28 

41.98 
47.13 

42.85 
47.98 

43.71 

48.82 

44.57 
49.66 

45.43 

50.50 

0.8G 
0.84 

0.06 
0.07 

162 
161 

1960 
1970 

U.V/3 

0.254 

14 
25 

19 

1  51.33 

52.16 

52.98 

53.80 

54.61 

55.42 

0.82 

0.07 

160 

1980 

0.223 

30 

20 

-1  56.23 

57.04 

57.84 

58.64 

59.43 

60.22 

0.80 

-0.07 

159 

1990 

0.  182 

44 

21 

2     1.00 

1.78 

2.56 

3.33 

4.10 

4.86 

0.77 

0.08 

158 

2000 

-0.134 

+  51 

22 
23 

2     5.62 
2  10.08 

6.37 
10.81 

T.12 
11.54 

7.86 
12.26 

8.60 
12.98 

9.31 
13.69 

0.74 
0.72 

0.08 
0.08 

157 
156 

2010 
2020 

0.080 
-0.023 

58 

24 

2  14.39 

15.09 

15.79 

16.48 

17.17 

17.86 

O.G9 

0.09 

155 

2030 
2040 

+0.036 
0.093 

58 
55 

25 
26 

-2   18.54 
2  22.51 

19.22 
23.16 

19.89 
23.80 

20.56 
24.44 

21.22 
25.07 

21.87 
25.70 

O.GG 
O.C3 

-0.09 
0.09 

154 
153 

2050 

+0.146 

50 

27 

28 

2  26.32 
2  29.94 

26.94 
30.52 

27.55 
31.10 

28.16 
31.67 

28.76 
32.24 

29.35 
32.81 

0.60 
0.57 

0.09 
O.l'O 

152 
151 

2060 
2070 

u.  iy.i 
0.231 

33 

29 

2  33.38 

33.94 

34.49 

35.04 

35.58 

36.11 

0.54 

0.10 

150 

2080 

0.25!) 

23 

30 

-2  36.64 

37.16 

37.68 

38.19 

38.70 

39.20 

0.51 

-0.10 

149 

2090 

V.X'l'l 

+  12 

31 

2  39.70 

40.19 

40.68 

41.16 

41.64 

42.11 

0.48 

0.10 

148 

2100 
2110 

+0.282 
+0.275 

-   1 
-13 

32 

33 
34 

2  42.57 
2  45.25 

2  47.72 

43.03 
45.68 
48.11 

43.48 
46.10 

48,49 

4393 
46.52 

48.87 

44.38 
46.93 
49.25 

44.82 
47.33 
49.62 

0.45 
0.41 
0.38 

0.10 
0.10 
0.11 

147 
146 
145 

35 

-2  49.99 

50.35 

50.70 

51.05 

51.39 

51.72 

0.34 

-0.11 

144 

36 

2  52.04 

52.36 

52.68 

52.99 

53.30 

53.60 

0.31 

0.11 

143 

Multiples  of  the  Period 

37 

2  53.90 

54.19 

54.47 

54.75 

55.02 

55.28 

0.27 

0.11 

1  12 

nf  this  El/nation. 

38 

2  55.54 

55.79 

56.01 

56.28 

56.52 

56.75 

0.24 

0.11 

141 

39 

2  56.96 

57.18 

57.39 

57.60 

57.80 

57.99 

0.20 

0.11 

140 

40 

-2  58.17 

58.35 

58.52 

58.69 

58.85 

59.01 

0.17 

—0.11 

139 

1 

302.  1 

41 

2  59.17 

59.  32 

5!).  16 

59.59 

59.72 

59.84 

0.13 

0.11 

138 

2 

604.8 

42 

2  59.94 

60.05 

60.15 

60.25 

60.3  I 

60.42 

0.09 

0.11 

137 

3 

907.2 

43 

3     0.50 

0.57 

0.64 

0.70 

0.75 

0.79 

0.05 

0.11 

136 

4 

1209.6 

44 

-3    .0.83 

0.86 

0.89 

0.91 

0.93 

0.94 

0.02 

-0.11 

135 

5 

1512.0 

GO' 

50' 

4O' 

30' 

20' 

10' 

Arg. 

6 

1814.4 

7 

21J6.8 

8 

2419.2 

NDTK.  —  When  the  degrees  of  the  Argument  are  read  from  the  right  band  side  of  the  Table, 

9 

2721.6 

the  tens  of  minutes  must  he  read  from  the  bottom;  ami  the  Reduction  and  its  Secular  Variation 

are  affected  with  the  sign  -|-  instead  of  —  .              • 

TA1IL.K  XL,  VI. 


81 


/,'•  iliicliiiii  la  l!u-   /•>//////!•  /'in-   1S.">(). 

Ar;;ii  in  =  Orliit  Longitude  -f-  (:!UO°  —  Q),  or  this  angle  diminished  l>v   1 

Aff. 

0' 

10' 

20' 

3O' 

10' 

50' 

Diff. 

for  III'. 

V.-,r.  in 
ion 

0 

16 

-3     0.95 

o'-'i  i 

0.93 

// 
0.91 

II 

0.88 

0.09 

-o'l  i 

o 

184 

Hi 

3     O.S5 

0.81 

0.77 

0.72 

0.66 

0.59 

0.05 

0.11 

133 

47 

3     0.;»2 

0.11 

0.36 

0.27 

0.18 

0.08 

0.09 

0.11 

139 

48 

•2  59.9N 

59.8T] 

68.75 

59.63 

59.50 

5!).  36 

0.13 

0.11 

131 

19 

2  59.21 

59.06 

5S.90 

58.74 

58.67 

68.40 

0.1G 

0.11 

130 

50 

-2  5N.23 

68.05 

57.86 

57.66 

57.  Ml 

57.26 

0.-20 

-0.11 

189 

51 

2  57.03 

56.80 

56.57 

56.3  1 

56.10 

55.S6 

0.94 

0.11 

128 

52 

2   55.61 

55.35 

55.09 

54.82 

51.51 

64.96 

0.87 

0.11 

127 

58 

2  53.9N 

58.69 

58.88 

53.09 

52.78 

52.  16 

0.31 

0.11 

126 

54 

2  52.11 

5  LSI 

51.48 

51.14 

50.80 

50.  15 

o.:ti 

0.11 

126 

65 

-2  50.09 

19.73 

49.36 

48.99 

48.61 

48.22 

0.38 

-0.10 

194 

56 

.  }       \~r  QO 

47.48 

47.03 

46.62 

46.2  1 

45.79 

0.41 

0.10 

123 

57 

2  45.37 

11.91 

44.51 

44.07 

43.62 

13.16 

0.44 

O.JO 

122 

58 

2  42.70 

•12.23 

41.76 

41.28 

40.80 

40.32 

0.48 

0.10 

181 

59 

2  39.84 

39.35 

38.85 

38.35 

37.84 

37.32 

0.51 

0.10 

120 

60 

-2  36.78 

36.25 

35.72 

35.18 

34.64 

31.09 

0.54 

—0.10 

119 

61 

2  33.53 

32.97 

88.41 

31.81 

31.27 

30.69 

0.57 

0.09 

118 

62 

2  30.09 

29.50 

2N.91 

28.31 

27.71 

27.10 

0.00 

0.09 

117 

68 

2  26.  17 

25.85 

25.22 

24.59 

23.95 

23.31 

O.G3 

0.09 

116 

64 

2  22.67 

22.02 

21.37 

20.71 

20.05 

19.38 

O.G6 

0.09 

115 

65 

-2  18.69 

18.01 

17.33 

16.64 

15.95 

15.25 

O.G9 

-0.08 

lit 

66 

2  11.55 

13.84 

13.13 

12,41 

11.69 

10.97 

0.72 

0.08 

113 

87 

2   10.21 

9.51 

8.77 

8.03 

7.29 

6.54 

0.71 

0.08 

112 

68 

2     5.78 

5.02 

4.26 

3.49 

2.72 

1.94 

0.77 

0.07 

111 

69 

1  61.16 

60.38 

59.59 

58.80 

58.01 

57.21 

0.79 

0.07 

110 

70 

-1  56.39 

55.58 

54.77 

53.95 

53.13 

52.30 

0.83 

-0.07 

109 

71 

1  51.48 

50.65 

49.82 

48.98 

48.14 

47.29 

0.84 

0.07 

108 

72 

1  46.44 

45.59 

44.74 

43.88 

43.01 

42.14 

0.8G 

0.07 

107 

73 

I  41.26 

40.39 

39.51 

38.63- 

37.74 

36.85 

0.88 

0.06 

106 

74 

1  35.96 

35.07 

34.17 

33.27 

32.36 

31.45 

0.90 

0.06 

105 

75 

-1  30.54 

29.63 

28.71 

27.79 

26.87 

25.95 

0.92 

-0.06 

101 

76 

1  25.02 

24.09 

23.16 

22.22 

21.28 

20.34 

0.94 

0.05 

103 

77 

1   19.39 

18.44 

17.49 

16.54 

15.58 

14.62 

0.95 

0.05 

102    " 

78 

1   13.66 

12.70 

11.73 

10.76 

9.79 

8.82 

0.97 

0.05 

101 

79 

1     7.84 

6.86 

5.88 

4.90 

3.92 

2.93 

0.98 

0.04 

100 

80 

-0  61.94 

60.95 

59.96 

58.96 

57.96 

56.96 

.00 

-0.04 

99 

81 

0  55.96 

5  1.96 

53.95 

52.9  1 

51.91 

50.93 

.01 

0.03 

98 

82 

0  49.92 

48.91 

47.90 

46.86 

45.86 

II.  si 

M 

0.03 

97 

N3 

0  43.H1 

42.79 

41.76 

40.71 

40.71 

39.68 

M 

0.03 

96 

M 

0  37.65 

36.62 

35.58 

34.55 

33.52 

32.48 

.03 

0.02 

95 

85 

—0  31.45 

30.42 

29.38 

28.34 

27.30 

26.26 

.04 

-0.02 

91 

86 

0  25.21 

24.17 

23.13 

22.08 

21.03 

19.98 

.or, 

0.02 

93 

87 

0  18.93 

17.88 

16.83 

15.78 

14.73 

13.68 

M 

0.01 

92 

88 

0  12.63 

11.58 

10.53 

9.48 

8.42 

7.37 

.05 

-0.01 

91 

89 

-0    6.32 

5.27 

4.21 

3.16 

•2.  1  1 

1.05 

.05 

0.00 

90 

60' 

50' 

40' 

30' 

90* 

10' 

Arg. 

NOTE.  —  When  the  degrees  of  the  Argument  are  rend  from  the  right  hand  side  of  the  Table,  the  tens  of  minutes  must  be 

read  from  the  bottom;  and  the  Reduction  and  its  Secular  Variation  arc  affected  with  ihe  sign  -f-  instead  of  —  . 

UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


1952 


LD  21-95m-ll,'5Q  {2877816)476 


Hinder 

i.)l.irJ    H">-  •   I'"' 

M«k*n 

Slucklnn.    Calil 
,188 


-Lo.uj.as    or 


v  or.uo . 


-/; 


U  C   BERKELEY  LIBRARIES 


i»' inn  innilin  Mil  illillllli  III  lllli  Illlil 
CD37M7bDas 


1937 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


